In my experience with the A7 ASHP waterheater, that ice cold air goes right to the basement floor.
That area of the basement has no floor covering at all.
Right after a heat pump run, the floor is slightly colder than other areas in the basement.
But, within a few hours, the floor surface temperature is back to normal..
My slab is a Geo-source of "heat"..
And of course during August, that slab is my Geo-cooling source..