I previously related a recent episode where I stopped on a steel bridge in sub zero weather to take some sunrise photos and my feet froze (well, not literally). I rode for about 1/2 hour without them rewarming and they only got better when I stopped and walked my bike for about 5-10 minutes. I also think it was the fact that the foot stays pretty stationary on the pedals and that thicker socks only really work in a roomier shoe.

I used to ice climb a lot and it was pretty common to spend most of the belay kicking and wiggling my toes even in a thickly insulated boot.