First thing first, if you ride with clipless pedals buy a pair of winter riding boots. You can spend tons of money on shoe covers, but they won’t work as well and it will just annoy you that you spent $150 on assos shoe covers that fall off and leave your feet cold. I use Shimano MW-02 winter shoes.
Next I will throw on a shoe cover if it is below 15°F out, I like Sidetrak booties, but they are no longer being made.
To keep your feet warm on the ride, you need to start with two things; warm feet and warm shoes. If I am driving I keep my shoes up in the front seat footwell so they start off warm. If I am at home I leave them in front of the heat vent. Why waste foot warmth warming up the shoe with your foot?
But then you need to start with warm feet, this might seem ridiculous and it probably is, but it works for me…. While getting suited in my space man riding costume I wear down booties from Sierra Designs.
This is what works for me, hopefully it’ll help you out too.
FYI I've found the Endura MT500 shoe cover to be the best thing I've ever found. Warm, well made and very walkable.