Yes, many people leave their hot tub outside during the winter either drained, winterized, and covered or for use all winter. If you do not mind the higher electric bill, there is no reason you cannot have your outdoor hot tub running and ready to use all winter. Make sure to keep the power on, the water levels normal, and ensure all the equipment is functioning properly and there is no danger of your pipes freezing. Also, be sure to use a spa cover when you are not using the hot tub to keep outdoor weather and debris from entering the spa.