Colds actually have many many different strains, but none of them are retroviruses. A retrovirus inserts it's own DNA analog into the host nucleus, so the host cells make more virus RNA. The best example of a retrovirus is HIV. Yes, it's very difficult to make a vaccine for that.

We can make cold vaccines quite easily. It's decades-old technology. And they work fine. BUT (and it's a huge but) they only work against that strain. There are a hundred+ other strains that will cause more colds. In fact we sort of do that, by making antibodies against a strain we catch. Then we can't catch that strain for a while, a few years to a lifetime. So it's not that we can't make such a vaccine: It's just useless and making it would have no return on investment.