I know the correct answer here, but I wanted to raise the question because my definitions are nonstandard. That is, mine are dependent somewhat on what the item is made of.

If your hand-warming garments have one big pocket for all the fingers but are made of leather or are otherwise weatherproof, I'm just as likely to call them gloves as mittens. And if they have individual fingers but are knitted, I'm probably going to call them mittens.