I got pretty used to as much as 25% less range when really cold, below freezing. But that was with a completely un insulated, metal box to carry the pack. Just insulating it would get back closer to losing only 10% or so.
Insulation, then the hot hands under it could work well. But not so great if the pack ever really reaches frozen state. It's just a lot of mass to thaw by then. So try to concentrate on insulation mostly, so the pack never really gets that cold in the first place.
If you need that hot pack every day to make it home, the answer is even simpler. You just need a larger battery in winter.
Using the battery voltage to heat up the battery is not ever going to make you have range. That's what a cold battery does anyway. It has high resistance when cold, and uses those lost watt hours warming itself up to a temp where resistance is lower.
But if you can park where you can plug in an AC powered battery warmer, that would be ideal. Or, just bring the battery in, so a warm battery in an insulated box or bag is all you need to have decent performance in cold weather.