I agree with what's been said about getting boots big enough to allow uncompressed insulation layers next to your feet. Unfortunately boots often get longer/wider with increased size but the height isn't affected proportionally. You need insulation between your foot and the ground.
Here's the Canadian military version of the mukluk:
Note the tall foot/toe box which leaves room for the permeable footbed, the crazy thick insole, and the liner. That footbed is meant to trap ice. The moisture in the air around your foot freezes towards the bottom of the boot where it's coldest next to the ground. Not important if you're only out for a few hours perhaps but if it's all day, or days, it allows you to knock the ice free, reinsert, and have happy feet again the next day.
Here's a close up view of that footbed showing how permeable it is:
The liner is actually two liners sewn together:
The boots I've been using this year are work boots meant for cold weather use.
A thick sole and tall foot/toe box for insulation. The similarity in footbed is no accident. I've worked in these boots at -45 C (-49 F) for extended periods and never had cold feet as long as I was moving even a small amount. Motionless in a stand is a tall order though. Move a bit if you can, put on another hat. I think heated clothing (socks, insoles) may be a great option though I've not used them myself.
Cheers, Greg