In the old days, before I moved south, I would plow a huge track the width of my tractor bucket in a field and then spread my manure on it...it sounds crazy but the footing actually wasn't that bad and at least I could exercise the horses in winter.
You could try some round pen if you access to one. What I like to do when my horse and I can't really do much is either try liberty or make boredom busters. Boredom busters are a way to keep your horse occupied during the days you can't ride. I've made carrots and apples on a string, you could put treats in a milk jug and have your horse try to get them out, and you could also poke holes through a two liter, put treats in it, and hang it in your horse's stall and they can play around with it and try to get the treats out. As for liberty, there are tons of ideas on Youtube and you could also do trust building. Hope I could help!
Our border has taught her horse to stretch. She stands by his side and he reaches his neck around to grab the treat. It helps to keep them flexible and gives their mind something to do. I do this sometimes with my guys and also hold the treat inbeteen their forelegs to get their top line stretched.
I would try and hand-walk him. It may be super cold but it's good if you can just bundle up and go for a walk to occupy him for at least fifteen minutes. Maybe get him some toys or give him hay in a slow feeder.