So our upstairs game room has a musty smell on the few fairly rare occasions we've run the AC this winter. Of course we usually run the heater. That doesn't ever smell. But on the occasion That we run the ac for a cycle on days that the heat just gets up a bit in the upstairs, it smells.

Don't remember it smelling ever during summer

The same ac doesn't seem to smell in the two bedrooms upstairs.

The heater runs daily (through the same vents and same heat pump) and I don't smell it.

Any thoughts?

Maybe dirty sock syndrome. Google it.

Milwaukee's likely right. Very well could be dirty so I syndrome. The smell will go away if you keep the ac on for a few days but will be back as soon as you go to heat. I've had some luck spraying Lysol into the return air while the fan is running.
There are chemicals made for treating it but to be honest I've had the same luck with Lysol as I have expensive chemicals.

Not saying this is the problem but we had black mold in our up stairs AC vents. The builder evidently didn't seal the vent boxes and it was sucking in moisture from the attic which provided a breading ground for black mold. Not sure what the mold was feeding on but it was visible on the vents after several years.