Sometimes it is, it depends on the virus causing it.

Do you have any examples of retroviruses that cause the common cold? I did a quick search but couldn't find anything, but that sounds like something that would be really interesting to read up on - the classical retrovirus isn't necessarily something that can go away after a couple days of sniffles and I'm curious to know if there are long term consequences to colds caused by retroviruses.

The search results are probably flooded, if you need good info look for anything from before the resent outbreak. Its on the wikipedia page for common cold, I think I got the factoid when I was searching google patents for coronavirus (might be interesting to check out as well) https://en.m.wikipedia.org/wiki/Common_cold#Viruses

I don't think coronavirus is an integrating retrovirus? It's an RNA virus for sure, but I haven't ever heard of it causing genome integration, and it would probably be a lot more dangerous (ability to cause cancer for instance) if it did?