I wouldn't bring it up. My DD2 had a constant snotty nose for most of her first year. She caught cold after cold after cold. She would clear up for a couple of days, maybe a week and then it would start again. I didn't take her to a Dr. What could they possibly do? There is no cure for the common cold that I am aware of.

You could suggest the teacher gets someone in to do a health lesson on blowing noses and washing hands before the start of winter bugs.