Instead of wearing gloves or mittens, both of which send the baby into an apoplexy, and which she removes and throws split seconds after being adorned with them, I put socks on her arms instead. Last winter when she was less than one, I put on a pair of her older sisters’ ordinary socks. Because they fitted the baby right up to her arm pits she couldn’t take them off and she had a least some protection from the cold when she was in the buggy.
This year she has learnt to pull ordinary socks off with her teeth. What does work now are thick welly socks. These are much warmer and thicker and so are much more snug-fitting on her arms. She seems happy to put them on, they are much harder to pull off anyway, and when we arrive at our location, she doesn’t have frostbite on her fingers.
In a related tip, baby socks are also rubbish on baby feet. Babies, it seems, just want their hands and feet bare. Anyway, I have found that it is better to dress the baby in tights, whether she is wearing skirts or trousers. Tights stay on baby feet/legs and baby socks just don’t.