My feet would get cold very easily as well. After foot surgery on each (unrelated to cold!), it got worse due to poorer circulation. What I used to do was toss a hand warmer in my boot, then after an hour or two, change it out for a hot one. That was a pain.
Then I tried the Artic Shield OVER my boots, with hand warmers, without much luck. Then I took my boots off, and put my foot, along with hand warmers, in the AS. Worked pretty good.
Last week in SD, it was 5 degrees, and my AS were still in TN. So, I put two toe warmers inside my first sock. Then 2 handwarmers inside my second sock, and a third sock over that - thick socks. And I stood on some cushions I had brought for sitting so the socks didn't get wet. So there I stood, 5 degrees, in my sock feet, and it worked!
The key to it is the handwarmers and toe warmers have to get oxygen to work. There's no oxygen in a boot, so you have to replace it with something that breathes. I've also used the felt liner from a Pac Boot, taking the PB off so the TW's and HW's can breathe.
I've considered the battery operated Thermacell(?) insoles, but they're a little pricey for something I'm not sure will work. Like the electric socks I bought years ago. Big waste of money!
Good luck!