Most kids get an average of six colds a winter.
While you cannot prevent them, hand washing frequently, hand sanitizer when no soap is available, keeping toys wiped down after a cold has passed, teaching coughing in their elbows (not covering their mouth with their hands) will really reduce the chances. I do part time child care so I have all kids remove shoes when coming in and head straight to washing hands before anything. Once a week I wash down and sanitize the toys.
This winter has been a great deal easier as far as nobody getting sick like last year. I mean both kids are a lot healthier this year.
I also will give children's airborne with the first onset of symptoms and that has seemed to help greatly. Talk to your Pediatrician first though as your kids may be too young. I also take it when they get sick for adults so I can stave off getting it. Make sure hand sanitizer is used after blowing noses, you and them, put tissues in the trash before you clean your hands.
Extra Vitamin C, keeping them hydrated, humiditity in the air while they sleep is essential to helping them stave off illness.
The more illness now it will build up their immune system though it is hard to see your little ones sick. Promise. I have a seven year old that was sick a lot between 2 and 5 and now hasn't missed a sick day of school in almost two school years! :)
You don't need to rush them to the Dr by any means unless they have a croupy cough/deep chested for more then three or four days, if they have a fever of 101 or greater for over 24 hours, throwing up for over 24 to 48 hours or complaining of severe headache or ear pain.
Otherwise, just treat the cold with Vick Vapor plugs, vapor rub and hydration/vitamins. Most kids don't even need a daily vitamin unless they are picky eaters. The only time I do vitamins is if my kids are sick as they need that added nutrition factor.
Don't rush them in either, see if you can just call the on call dr or nurse during the day, give them the symptoms and see what they think. It will save you a ton of money! :)