I've never hurt myself skiing, it really isn't as dangerous as its made to be. As for the cold, you obviously wear a thick coat, and you heat up skiing so you don't notice it anyway; its an interesting experience as well, being in very cold conditions. In skis nowadays there is a tolerance system whereby if the binding is under pressure, as happens in most falls; the ski will detach from the boot to prevent injury.

It can be expensive, but there are a few very good resorts with cheap prices in the off-peak months.