Hey there - I'm upstate NY but originally from Canada.
You're feet will get cold doing nothing, it's a fact. BUT, you must wear wool. not even those thinsulate socks at $15 a pair compare. Cotton & sweat will do more damage at the end of the day if you can't re-warm dry.
2nd thing, those Sorrel skidoo boots are awesome, but not good walkers. Don't expect to hike in them, but they're the best for warmth.
3rd, those little heat packets are wicked.
4th, wiggle & flex those little piggies!