I used to work for a big hardware company and we regularly sold heated jacket that just accepted tool batteries. For example our Milwaukee jackets just accepted the Milwaukee tool batteries. So when you’re on the worksite you just swap out and recharge the batteries as needed with all of the other tool batteries. I got one of those jackets myself once and they are super nice. It could toggle between 3 different power levels depending on what you needed and the battery actually lasted a surprisingly long time.
As far as the rest of your body goes just layer up. Long wool (or goretex if you have the money for it,) socks, long underwear, thermal pants, boots, gloves, ski mask, and maybe an additional hat plus your coat hood. Of course you also want torso layers with the heated jacket but if you’re using one of those then it will be doing most of the heavy lifting as far as keeping you warm goes. If you frequently get cold feet/hands then you can also add glove liners and an extra pair of socks or just toss some instant heat packs in your socks and gloves as needed (they normally last several hours).
Also when it comes to your inner layers avoid cotton like the plague. The saying in boyscouts was always “cotton kills” because even though cotton is insulating, it loses all of its insulating properties the moment it becomes even slightly damp and it will not dry on its own. When it gets wet, wearing cotton is worse than wearing nothing at all. I personally made that mistake once and I was literally better off once I pulled off my socks and just walked around with my bare feet in my boots. When it comes to fabric choice the ideal choice is wool because it’s insulating and getting a little wet doesn’t impact that too much. But if all you have are synthetic fabrics then go with those; they typically don’t insulate as well but they still work better than cotton when they get wet. If you have the money and feel like splurging, goretex is a synthetic fabric that is supposed to be even better than wool; I’ve never gotten the opporitunity to try it out though so I can’t say much there.