Being plagued by moist air during day does cause problems with ASHPs.
(At just above freezing)
ASHPs also have icing problems, when sucking in snow during heavy snow fall.
One of my problems was rain (during cold weather) dripping down the wall
and splashing into the coil.. Sealing out the water from above should work for me.
I'm lucky because this condition occurs very rarely.
Your idea of storing solar heat during the day and using it at night makes good sense for your local weather.
Just hope there isn't an underground river effect pulling your solar heat away, downhill..
A solar storage tank could be the other option..
Cheers,
Rich