This should be your main concern when going for the occasional winter ride. Wet, sweaty hair loses its insulating properties and can give the horse a chill. Be sure your horse is completely cool and DRY before you turn him loose again. For those of us who ride all winter, there are several things we can do to make winter riding less stressful for our horses. The first of which is to adjust our riding routine to include extra long warm up and cool down time.
Cold muscles take longer to stretch and flex.
Some riders ride with a saddle blanket that also covers the hindquarters of the horse. Cooling down will take longer and is much more important during the winter months. It can be beneficial to offer your horse tepid water instead of ice cold water while cooling down from a really hard ride. Clipping some of the horse's winter coat will reduce cooling off time. This is a healthier alternative than heavy blanketing to keep a winter coat from growing, although you will still need to blanket once you clip.