As far as I know, people suffer from the cold since ever. Why didn't and don't we evolve to resist it?
The main reason is that there really isn't any one "cold," but rather the word is used to describe many different infections that simply have the same symptoms. The reason for these same symptoms is that almost all of the symptoms that one experiences in a cold are actually the immune response to said infection. For instance, a fever is used to make the body less hospitable for the infection causing agent and throwing up is used to ensure that harmful substances are removed from the digestive system before they can cause too much harm.
The reason that the body can't simply evolve resistance to all of these possible infections is both because the infections evolve too and because there are simply too many of them that all need a separate method to be defeated. Therefore, curing the common cold is effectivley curing the majority of known ailments.