Depends on the shoe in feeling "colder" for me. If shoe has less non-breathable material, then my feet are warmer. I have new pair which I like (and feel more powerful on my pedal stroke because the soles are stiffer) but has more breathable material.

I have rain cover booties but haven't worn them yet. And I do cycle in rain, winter (when very little ice, snow). It's a challenge to cycle for hours when the temp. rises up to 20-25 degrees C higher over the course of several hours. It's a "problem" in so far, I don't like carrying so much clothing when cycling within the city, but I have to.