Having been a feedlot pen rider up here in Allberta, riding in the winter was part of the job. Colder the day, longer we were on the horses. Proper warm clothing that allows freedom of movement is essential. I love my Carhart gear. For footwear I have my winter riding boots, larger size so room for thermal socks. Feedlot horses wore borium shoes and snow pads but that is a huge expense. I now keep my horses barefoot in the winter and compete every weekend.
Like others have said, make sure your horse is cooled out and dried off before you turn them back out after you ride. Sweat blankets work great.