I actually wear some waterproof trail running shoes for walking in icy weather. You have to be a bit careful what you step in obviously, since they're not high

I actually wear some waterproof trail running shoes for walking in icy weather. You have to be a bit careful what you step in obviously, since they're not high tops, but they're thick enough to walk on ice without it getting to you. Boots are overkill and walking in snow is just too slow to get exercise anyway, so you end up only walking on the cleared streets and sidewalks.