[vikramkr]

This has been considered as a potential factor in explaining the variability in COVID outcomes for a while, both in the sense that prior infection with a cold virus could help protect from COVID through T cell responses and could make COVID worse through antibody responses. Cytotoxic T cell responses are definitely good, and it's also good to know that coronaviruses can induce these sorts of long term immunities (so a low antibody response doesn't automatically mean you're susceptible to reinfection). The COVID vaccines in development are also generally trying to induce T cell responses, and knowing that coronavirus epitopes can do that is a really helpful data point in determining the feasibility of that goal.

[amluto]

I've also heard a hypothesis that infection with a common cold at the same time as COVID-19 could improve the outcome. The idea is that COVID-19 seems to suppress interferon production in infected cells but does not seem to suppress the response to interferon from outside the cells. So, if you have a normal cold, your lungs and/or airways might contain interferons, and those might help your innate immune system defend against COVID-19.

This hypothesis is entirely untested as far as I know.