For the issue of "fingers are cold but gloves affect mobility", purchasing a pair of thumbhole arm warmers have made a world of difference for me

They're almost like fingerless gloves, but more comfortable and easier to manage.

You might be worried "but it's the fingers that are cold anyway, so fingerless gloves are not what I need." I thought that too, but trying them immediately proved me wrong and I never had an issue with cold fingers again. I'm fairly sure it's because warming your wrists/palms keep your blood from losing heat in those areas, so your fingers get much warmer circulation.

For something less than $10, it's probably the best purchase I've made for working in the winter