A cold is a virus, w/ variants, as many explained above you could get other viruses. Also! It would in no way protect you from a bacterial type infection, and it could make one more likely to take hold on your nasal passages (sinus infection) or brachial passages (bronchitis).

As a kid, I was the person who got a sinus infection after every cold. It’s much better nowadays and I also get far fewer colds because I am much better at germ avoidance than I was in school.