I think it depends on what you can do. Spin? Knit? Felt?
If you know how to spin and knit then you could spin a thick mitten, or even just a bag with a drawstring at the wrist if he's not using his hand much (would keep the thumb warmer). If you can knit but not spin you can draw fleece out into a thick length and knit it into a mitten or bag on large needles. If you can felt, make some thick felt and make a bag or mitten from that. If you can knit and felt, then knit an oversize mitten and felt it down until it's the right size. Or, if you have a not too thick sheepskin, you could cut that up and make a mitten or bag with the woolly side in. If he were to wear a thin silk glove inside the mitten that would help a lot - silk gloves are available in motorbike shops for not too much
Or, you can get heated gloves (in motorbike shops for example) and blocks which you keep in your pockets and when you bend them they give off heat (maybe in fishing shops)