I used to teach XC skiing to little'uns. As you can imagine, for me there was a lot more standing around than skiing, and my feet would freeze even at mild (warmer than -5C) temperatures.
The solution for me was chemical toe-warmers - remove them from their plastic pouch and stick them to the insoles of my boots near the toes, and my feet would be warm for hours. I don't know if this is practical for OP's use, like would be a bit of a pain for daily commute x2 directions..