I use these while walking in and out - while I'm moving i get plenty warm so my hands normally don't get cold.
https://www.basspro.com/shop/en/redhead-camoskinz-liner-gloves-for-men
Once I settle in I keep those on and use this
https://www.basspro.com/shop/en/redhead-insulated-fleece-handmuff
With some hot hands or a rechargeable zippo hand warmer
https://www.amazon.com/dp/B07Q6GQM9D/ref=cm_sw_r_cp_apa_fabc_aIhVFbD6P7NHA
The glove liners have those small rubber nubs on them so gripping the firearm is nice and easy.
I'm in NH and last season we saw single digits and that system worked great. This year is mild so far so I've only broke out the give liners a few times - they are warmer than you'd think.
Rechargable hand warmer and back up battery - quick heat for sore joints and you can charge your phone with it.