It could certainly be a lot of different things.

I was having similar problems a year or two ago when I was doing a lot of cross-country skiing (not currently a problem since it's still downright summery for December on the East Coast). I attributed things to carpel tunnel (compression of the median nerve) or ulnar nerve compression. If you bend your wrist when you sleep (something most of us do without thinking about it) it puts more pressure on the nerves.

I found that sleeping with wrist splints helped (you can get these over the counter- just tell them you're looking for a splint for carpel tunnel). Again, it could be a lot of things, but if it seems to be mainly coming from the hand and you're avoiding going to the doctor, the wrist splints might be worth a try (just try them on before you buy them- the sizing can be a little funny).