Thanks MacG. I tried it with the wool cap, last night. It was a bit drafty.
So, I tried a wool sock pulled over my cast, this morning.
It was worthless.
I then wrapped a scarf around my hand and then put the sock over that.
A little better, but still pretty dang chilly.

Tomorrow, I'm going to just take the whole contraption off, put a glove on and then put the splint on, over it. It's a half-cast, held on with an ace bandage, so I can take it off as needed.