I have used chemical warmers for CX races and carry some in my pockets for very cold days. I bought winter riding boots (Gaerne Akira for the road; Northwave Extreme Winter GTX for gravel on my CX bike) a while ago, and never looked back. Those boots are spacious enough to put warmers if needed.

In my CX shoes, in the winter, to insulate from the cleats, I cut a couple of extra "insoles" -- one is of the plastic backing you put under a tablecloth (plastic on one side, fleecy in the other) and the other 'insole' is cut from a mylar blanket. I put the plastic one at the bottom, then the mylar and last the normal insole on top. I have not had to worry about that in this area: we don't have races when it's 12 degrees outside, but that helped in Chicago.

I will add: Just beware of making your foot too tight in the shoe. Restricting blood flow is not good in the cold!