As for those saying that it's lack of blood supply, I disagree, I believe it's more nerve compression. If it was cutting off blood circulation, it would start to hurt pretty damn fast, and you'd wake up (or rather be woken up) with a painful arm, not a numb arm.
I think it can be either, No feeling but more worrying a cold arm with clammy skin. I doubt nerves can do that.
Although in some magazine or newspaper had the top 20 medical conditions blokes are worried about but don't seek advice. Dead arms from sleeping was in there. It said it did cause any long-term harm.