Shelter. If you don't have stables or your horse is happier out at grass during the Winter ensure adequate shelter is provided so that they can escape the elements as and when they choose. A shelter must be big enough so that all the horses or ponies in the field can get inside so that it's not just the dominant one/group that are able to keep warm and dry in the bad weather. If a man made shelter is not possible choose winter grazing that has natural shelter such as trees or dense hedges.
Observation. Don't just assume your horse is fine from a distance! Check your horse daily and thoroughly. Check their rugs, feet and limbs and that they look happy and healthy. Put your hand inside your horse's rug to check they are not too cold or hot. Have a look around the field to check there is no damage to fencing or potentially dangerous foreign object lying around.
Forage. Every horse needs adequate forage throughout the cold months as well as a constant supply of fresh (not frozen) water. If grazing is good then extra hay may not be required but if grass quality is poor or there is snow on the ground extra forage will be needed. Horses need different quantities depending on their age, health and work load. Don't forget, calories are spent keeping warm!
Rugs. Not all horses and ponies need a rug during Winter but sometimes it is necessary to keep a horse warm and dry with waterproof horse rugs for example older horses, horses that suffer with rain scald or mud fever and horses sensitive to the cold. Choose a well fitting horse rug and check the horse underneath regularly.
Clipping. Try to only clip hair off where necessary. Replace the clipped coat with an extra rug to compensate use a horse under rug or a full face horse hood to help horse stay warm after being clipped.