HAIR CUTTING IN ISLAM
Hairis the collection or mass of filaments growing from the skin of an animal, and forming a covering for a part of the head or for any part or the whole of the body or it is a filamentous biomaterial, that grows from follicles found in the dermis. Found exclusively in mammals, hair is one of the defining characteristics of the mammalian class. The human body, apart from its glabrous skin, is covered in follicles which produce thick terminal and fine vellus hair. Most common interest in hair is focused on hair growth, hair types and hair care, but hair is also an important biomaterial primarily composed of protein, notably keratin.
The word "hair" often refers to two distinct structures: 1) the part beneath the skin, called the hair follicle or when pulled from the skin, called the bulb. This organ is located in the dermis and maintains stem cells which not only re-grow the hair after it falls out, but also are recruited to re-grow skin after a wound and 2) the shaft, which is the hard filamentous part that extends above the skin surface. 
1 – Hair which we are commanded to remove or shorten. This is known as Sunan al-Fitrah, such as removing the pubic hairs, trimming the moustache and plucking the armpit hairs. That also includes shaving or cutting the hair of the head during Hajj or ‘Umrah.
The evidence for that is the hadeeth of ‘Aa’ishah رضي الله عنه who said: The Messenger of Allah (May Allah honour Him and grant Him peace) said: “Ten (actions) are part of the fitrah [natural inclinations of man]: trimming the moustache, letting the beard grow, using the siwaak (tooth-stick), rinsing the nose with water, clipping the nails, washing the finger joints, plucking the armpit hairs, shaving the pubes and washing oneself with water after relieving oneself.” Zakariyya said: Mus’ab said: And I forgot the tenth but it may have been rinsing the mouth with water. Sahih Al Muslim 261
2 – Hair which we are forbidden to remove, which includes the eyebrows. The action of removing the hair of the eyebrows is called al-namas. It is also forbidden to remove the hair of the beard. The evidence for that is the hadeeth of ‘AbdAllah ibn Mas’ood رضي الله عنه who said: I heard the Messenger of Allah (May Allah honour Him and grant Him peace) say: “Allah has cursed the woman who does tattoos and the one who has them done, the woman who plucks eyebrows (al-naamisah) and the one who has it done (al-mutanammisah), and the one who files her teeth for the purpose of beauty, altering the creation of Allah.” Sahih Al-Bukhari, 5931 and Sahih Muslim, 2125.
And it was narrated that ‘Abd-Allah ibn ‘Umar رضي الله عنه said: I heard the Messenger of Allah (May Allah honour Him and grant Him peace) say: “Be different from the mushrikeen: let your beards grow and trim your moustaches.” Sahih Al-Bukhaari, 5892 and Sahih Muslim, 259
Al-Nawawi (May Allah have mercy on him) said: The naamisah is the woman who removes hair from the face and the mutanammisah is the one who asks to have that done. This action is haraam, unless a woman develops a beard or moustache, in which case it is not haraam to remove it, rather that is mustahabb in our view. Sharh al-Nawawi, Sahih Muslim, 14/106
3 – Hair concerning which the texts are silent and do not say whether it is to be removed or left as it is, such as hair on the legs, hands, cheeks or forehead.
There is some difference of scholarly opinion concerning this:
Some said that it is not permissible to remove it, because removing it implies changing the creation of Allah, as Allah tells us that the Shaytaan said: “ ‘And indeed I will order them to change the nature created by Allah’” Qur’an.Surah Nisa’ 4:119
Some said that this is one of the things concerning which nothing was said, so the ruling is that it is allowed. It is permissible to leave it or to remove it, because whatever is not mentioned in the Qur’an or Sunnah is permissible. This was the view favoured by the scholars like Shaykh Ibn ‘Uthaymeen (May Allah have mercy on him), Fataawa al-Mar’ah al-Muslimah, 3/879.
(a) There is no sin on a woman if she removes hair on her upper lip, thighs, calves and arms. This is not part of the tanammus (plucking) that is forbidden.Fataawa al-Lajnah al-Daa’imah, 5/194, 195
(b) The Committee was asked:What is the Islamic ruling on plucking the hair between the eyebrows?
It is permissible to pluck it, because it is not part of the eyebrows.Fataawa al-Lajnah al-Daa’imah, 5/197 
A time limit has been prescribed for us for clipping the moustache, cutting the nails, plucking hair under the armpits, shaving the pubes, that it should not be neglected far more than forty nights, as mentioned in Sahih Muslim 497. 
For the one doing Hajj at-Tamattu’, then before entering the state of Ihram it is prescribed for them to do the following: take a bath, clip nails, trim moustache, remove unwanted hair (armpits and pubic) and wear two pieces of white cloth (towels/sheets). However, women wear “normal” clothing without wearing gloves or the Niqaab (covering face). As for the one doing Qiraan or Ifraad, they are already in Ihram so they cannot trim their hair or clip nails etc. 
Narrated by 'Aisha رضي الله عنه : An Ansari (belongs to Madina) woman gave her daughter in marriage and the hair of the latter started falling out. The Ansari women came to the Prophet Muhammad (May Allah honour Him and grant Him peace) and mentioned that to him and said, "Her (my daughter's) husband suggested that I should let her wear false hair." The Prophet said, "No, (don't do that) for Allah sends His curses upon such ladies who lengthen their hair artificially." Sahih Al BukhariVol 7:133,Vol7:818
Narrated Humaid bin 'Abdur-Rahman (May Allah have mercy on Him): That he heard Muawiya bin Abi Sufyan رضي الله عنه (talking) on the pulpit in the year when he performed the Hajj. He took a tuft of hair that was in the hand of an orderly and said, "O people of Medina! Where are your learned men? I heard the Prophet Muhammad (May Allah honour Him and grant Him peace)forbidding such a thing as this (i.e. false hair) and he used to say, 'The Israelis were destroyed when their ladies practiced this habit (of using false hair to lengthen their locks)." Sahih AlBukhari Vol 4:674, 694 and 7:816
Narrated Abu Huraira رضي الله عنه : Allah's Apostle said, "The Jews and the Christians do not dye (their grey hair), so you shall do the opposite of what they do (i.e. dye your grey hair and beards)." Sahih Al Bukhari 7:786and Vol 4:668, also in Sahih Al Bukhari, 3275 (NE) and Sahih Al Muslim, 2103.
Narrated Jabir ibn Abdullah رضي الله عنه : When Abu Quhafah (father of AbuBakr (R)) came in the Year of Victory or on the Day of Victory (to the Prophet Muhammad (May Allah honour Him and grant Him peace) to pledge his allegiance to him) his head and his beard were white like hyssop. He (the Prophet Muhammad (May Allah honour Him and grant Him peace)) commanded or the women were commanded by him that they should change this with something (that the color of his hair should be changed). Sahih Al Muslim
It was reported that Abu Umaamah رضي الله عنه said: “O Ansaar, dye your hair red and yellow, and be different from the A’aajim (Persians).” (Narrated by Ahmad, 21780
Narrated 'Ubaid Ibn Juraij رضي الله عنه : ...And about the dyeing of hair with Hinna; no doubt I saw Allah's Apostle dyeing his hair with it and that is why I like to dye (my hair with it). Sahih Al Muslim.
Many Muslims are unware of the fact that it is Prohibited (Haram) in Islam to change the hair color with black dye or black color. The Messenger of Allah (May Allah honour Him and grant Him peace) said: “The best things to use to change grey hair are henna and katam.” (Narrated by Tirmidhi, 1753; Abu Dawood, 4205; Ibn Maajah, 3622). Tirmidhi said: the hadeeth is hasan saheeh). Abu Bakr (may Allah have Mercy on Him) dyed his hair with henna and katam, Sahih Al Muslim, 2341. Katam is a plant from Yemen which produces a reddish-black dye. Henna produces a red dye, so when they are used together as a dye, they produce a colour that is between black and red. Fath al-Baari, 10/355. “Change this white hair but avoid black.” Sahih Al Muslim 5476
A stern warning was also narrated for the one who does that, which is when the Prophet Muhammad (May Allah honour Him and grant Him peace) said: “There will be people at the end of time who will dye their hair black like the crops of pigeons; they will not even smell the fragrance of Paradise.” Narrated by Abu Dawood (4212) and al-Nasaa’i Vol 8:138; classed as sahih by Al-Albaani in Saheeh Al-Jaami’ (8153). This indicates that it is haraam to change the hair colour to black. As for changing it to other colours, the basic principle is that it is permissible unless it is done in the manner of kaafir women or immoral women, in which case it is haraam for that reason, because the Prophet Muhammad (May Allah honour Him and grant Him peace) said: “Whoever imitates a people is one of them.” Narrated by Abu Dawood 4031 and classed as Sahih by Al-Albaani in Irwa’ Al-Ghaleel (5/109). 
Growing the beard is a wajib (mandatory) for all males who are capable of doing so. This has ample evidence in the Sunnah (traditons, Saying and actions of Prophet Muhammad (May Allah honour Him and grant Him peace)), and is the unanimous opinion of the ulemaa (Scholars) of Islam. One should not get misled by the neglecting this.
Narrated by Abu Sa'id Al-Khudri رضي الله عنه - The Prophet Muhammad (May Allah honour Him and grant Him peace) said, "There will emerge from the East some people who will recite the Qur'an but it will not exceed their throats and who will go out of (renounce) the religion (Islam) as an arrow passes through the game, and they will never come back to it unless the arrow, comes back to the middle of the bow (by itself) (i.e., impossible)." The people asked, "What will their signs be?" He said, "Their sign will be the habit of shaving (of their beards)." Sahih Al Bukhari Vol 9:651 and Fatul Al-Bari, Page 322, Vol. 17th, Book 93, Hadith 651 
  http://muttaqun.com/beard.html
 How to Perform the Rituals of Hajj and Umrah BY by Shaikh Muhammad As-Salih Al-Uthaimeen, http://www.princeton.edu/~humcomp/hajjguide.html