I've used a couple of mountain bike shoes with spd cleats. I've also got a pair of road shoes I put spd cleats on but they aren't as easy to walk around on.
Performance bike makes some shoe toe covers that just slip over the front of your shoes. That knocks a lot of the cold out. If you need more protection, there's booties to cover the entire shoe and foot or you can buy winter cycling shoes/boots. I wear some really thick wool socks (Defeet Blaze). Experimented with plastic wrap between two pairs of socks but that got very hot and sweaty.