You'll be fine, it actually might help cause itll get your lymphatics / blood flow going a bit more.
Just don't overdue it.
Vit C, Zing, B vitamins etc etc etc etc.
Just make sure you stay hydrated, it's easy to forget about water on the mountain. Really easy.
Nothing wrong with doing a few laps with a cold (as long as it's not serious). Just take it easy, drink water and once you get tired go home so you don't run your body down.
Also, taking vitamins after you get cold symptoms usually does nothing. It's a placebo effect for most people.
You need to be healthy and taking care BEFORE you get sick. Fyi, the most common vitamin deficiencies among snowboarders are vitamin d (lack of sunlight) and omega 3 (nearly everyone is lacking enough omega 3).
The reason is because studies done have been done when symptoms subside.
Symptoms arent the sickness, it's your bodies response to fight it.
So giving your body the tools to fight whatever you have = faster healing.
If your body is low in zinc, and you take zinc when you're sick. It will help you get better faster.
If you take Vitamin D when your'e sick, it will do nothing.
Saying vitamins only help in prevention isn't right.
Your body needs vitamins to make a proper immune response, if it doesnt have enough of it, what's it going to do?