Socks in the summer, slippers in cooler weather, like these:
But, I have wanted to find a pair of shoes with thin enough soles to be able to use them with heavy duty pedals like the HE Sprints. I have tried a couple of pairs of Adidas racing shoes, but the soles were too thick to have any kind of useful pedal feel for me. However, I think I have finally found a pair of shoes that will keep my feet warm in the winter while allowing for good pedal feel, and it's a pair of...wrestling shoes. Yeah, I know it sounds crazy, but have been testing this pair out the last few days, and they're working great.
These were $44 on Amazon and I'm going to keep them for the really cold weather this winter when the soft slippers just won't quite cut it in terms of keeping my feet warm.
Also, have found another pair of slippers for cool/warm weather that might edge out the fuzzy ones above. You can find these on Amazon as well for $20, and they are really well made slipper socks that have durability as well as great pedal feel with a very thin, flexible rubber sole:
Really impressed with these so far and will be testing them out more over the next days/weeks.