This is a time he will need to burn more energy to stay warm, therefore increase his ration of hay. Also, one of the most important things to check is that your horse has a clean, dry. A damp environment can lead to colds, coughs and viral infections. Poor ventilation can cause respiratory diseases while your horse can develop pneumonia of the stable is to hot or cold. If you don't have a barn, your horse should at least have a three sided shelter, open on the wind side down.
Most bedding can cause foot infections, so keep it dry.
Besides this, snow might be deep. Shoes should be pulled, because snow could call up badly in shod hooves. This makes it difficult for your horse to walk or run. Trim hooves enough so they won't crack or break, but not to short. As your horse paws through the snow he will wear them down, causing sore hooves if they are to short.