Years ago, I had the misfortune to be the Official Excavation Engineer for a ditch we had to dig in the middle of the winter. It was a lot of fun getting hit in the mouth by frozen clay chips with every swing of the pick-axe.
The first day left me with the worst case of froze-toes that I ever had. The guy I was slav, I mean, working under suggested that I try something he learned years before, when we was a sla, I mean the OEE.
Put on a pair of nice, heavy 100% cotton socks, then a pair of plastic bags, and then a pair of wool socks. (Of course, your boots must be roomy.) Yes, my feet were sweaty, but not a single bit cold. It really works, even with steel-toes.