Martyn is right ! The thing about reindeer fur/hair being hollow is exactly what makes it desirable ! The hollow hairs trap air, and insulates from the cold big time (the same thing with icebears) - a good skin should insulate at least as well as a thick Thermarest (I know as I use both).
The skin will shed hair as you use it. How fast this happends partly depends on the individual skin, but the main thing is at what time of the year the reindeer was killed and skinned. During winter the hairlayer is a lot thicker than during the summer. During autumn the hairlayer will get thicker, and during the spring the reindeer will shed hair preparing for the summer season.
Here in Norway a tanned reindeer hide from a late autumn bull costs about £ 44. A raw skin (no tanning - just dried) from a bull costs about £ 21. These are average prices for bull skins, female and calf skins are cheaper.
The skin most used as a sleepingmat is the dried and not tanned version. It is prepared by treating the fleshside with boiled linseedoil (several coats), which is allowed to dry. This skin will soak up a lot less water and is somewhat stronger than the tanned skin.