It could easily be colds due to exposure to more viruses via the preschool experience. But it could also be allergies. This is not an unusual time for them to start. My son started when he was 4 in preschool. His teacher even asked me if he could be allergic to something in the classroom, because his stuffiness and runny nose were accompanied by bouts of sneezing. (He would sneeze 3 or 4 times in a row, several times a day, and their "day" was only 3 1/2 hours long). He also started sneezing a lot more at home. He is 12 now, and is receiving immunotherapy (allergy shots) due to his continual battle with the runny nose. Which became a year round thing. Right now, there are a lot of things that can cause runny nose out.... goldenrod is in full bloom for instance.
If he doesn't act sick, just runny nose all the time, I would think it is more likely a pollen/mold/pet allergy. My son never felt bad from his allergies... just annoyed by the need for nose blowing and tissues all the time. Even people who so not consider themselves "allergic" to stuff, have drippy noses this time of year, and it is an allergy thing. But they have mild and short term drippiness, so probably assume they are fighting off a cold that never arrives. :)
If you can find local honey, a teaspoon every day can sometimes help. I know adults who SWEAR by it. Our son has so many different allergen triggers in the environment (including molds) that it didn't work for him. But it does for a lot of people.