A cold is caused by a virus so any amount of vitamins will make no difference to the cold at all, if what the scientists tell us is true! There are ways to strengthen your immune system which may help you avoid colds in the future but that is pure speculation because a virus can turn up anywhere anytime and, according to the scientists, be slightly different from the last cold virus you had, so you'll still get the cold!
Perhaps, at the end of the day, if you increase (say) your vitamin C or B you'll feel better about having a cold and the cold might disappear quicker?!?
I wish you good health whatever vitamin you take.