Yes, but they have this awesome system in their hooves. Researchers have discovered that horses have a shunt in the main vain at the back of their hoof, that shuts off the flow of blood to the hoof when the temperatures are really low. Then when hoof temp drops to a certain point, the shunt opens temporarily to allow warm blood to flow through it. Then it closes and on and on it goes to keep their hooves from freezing completely. That function is likely part of the reason why horses get laminitis.
So thinking about a steel shoe attached to the hoof, and steel nails driven into it, the steel, it would seem to me, would radiate the cold into the hoof so that system wouldn't function as efficiently. Shoes are a bad deal in the winter time especially in the snow.
I took this picture on a hike in the Little Book Cliffs, near Grand Junction, Colorado. We were looking for wild horses. We found them and it was kind of scary so I didn't get lots of great pictures. If you look closely, you can see the backs of two wild horses grazing on something. I'm not sure what they were eating out there. A little bit of everything I would imagine so that's why I like to feed my horses a variety of different hays. The brown and white horse is a stallion and he was a little bit snorty about us getting too close to his family. So we didn't.
So now I'm wondering if a foundered horse's hooves would freeze in the snow because the circulation in a foundered hoof isn't functioning normally....hmm. Or would the cold help them feel better. Somehow I don't think so, but I don't know?