I drive a 2009 2.4 LX CR-V with 80k under the belt. Why do I smell a musty smell from my HVAC only when it cools, not when it heats?

I thought the air flows through the cabin filters (imparting the smell) whether it's cooled or heated?

 

Mold on the air filter. If you run the ac all the time, and then park it, being damp and cold the cabin filter can develop mold. Sometimes it will also build up on the vent ducts. Have you ever replaced the cabin air filter? Mine use to do the same, after replacing the old moldy filter, and starting to turn the ac off about 1-2miles from home to help it dry out a little, I haven't had an issue since. My issue was on a 2000 CRV

 

You can also buy aerosol stuff that you can spray in your vents that neutralize w/ the smell. I got some at autozone and it works pretty well.