All of the hand sanitizer you own could not protect you from germs and particulate in the air that make you sick. During cold and flu season, which typically starts around December, bacteria, viruses, and other contaminants and irritants certainly don’t help the situation.
Your heating system has a blower fan that sucks in air from your home before heating it and blowing warm air back out. And with it, a lot of contaminants can recirculate as well.