DD is also in an inhome daycare 3 days per week, and she's been going there for almost a year. She's had a cold for most of that time, but fortunately...knocking on wood... it's never been anything more serious.
ETA: she did have roseola once and a weird bug that gave her a fever and mouth sore, was not Hand Foot and Mouth. But those both had very different symptoms than a cold.
Okay, this is exactly how DD is. It never, knock on wood, turns into anything more serious, but is pretty constant...poor thing.