There's oodles of batteries to choose from.
However, if your gloves draw 4 amps (and looking them up, one amp each is typical, so two amps each seems reasonable) that's about 50 watts. You'll need a big honkin' battery if you want them to last any amount of time.
For example, this
7 Ah 12 v battery weighs just under 5 lbs, and would power your gloves for under two hours. It would fit in your backpack fine, but you might not like it, especially if you need more than one to get the desired runtime.
A 3s LiPo pack would probably work well and could cut down the weight/runtime ratio considerably (probably by 50% or so), but would cost a good deal more. For example.
this would power it for a little more than an hour but weigh only a pound. You'd also need a $3 or so buzzer to warn you if the battery is getting low and a charger for it.
Back when I grew up in Anchorage, AK I just used ski mittens when it got really cold and that was fine. Mittens are a good deal warmer than gloves.