When your hands are cold making your fingers feel difficult to bend and move around. If they're hard to move around, you have crabby hands, your hands are crabby.
Comes from the
adjective crabby, meaning ill tempered, and from the likeness of your
cold hands to that of a crab, which has hard, plated hands with little freedom of movement. If your hands are crabby, they are misbehaving by being like a crab's hand. I'm guessing this is where it's from, I just
overheard a girl say it and thought "yeah that's the word for this".