Technically, but probably not both at the same time. What I mean
is that heat pumps in general tend to do one or the other quite
well, but not both. The problem is generally you are either
trying to heat up quite a large differential (because it's really
cold outside) or you are trying to cool down (when it's really
hot out). Heat pumps don't handle large differences well,
which is why folks who use them in hot regions tend to still
have their homes a tad on the warm side, or pay out the
wazoo for the energy. During cold spells, of which there
tend to be few, they allow the house to run a bit cold.
Heat pumps tend to have "emergency" heater strips (electric)
which kick in when the temp difference gets too big and
those burn ALOT of power.
I've found them in use far less in the north where it
gets cold because folks can easily be having to warm a
house up better than 40 or 50 F where as on the hottest
days in the south folks will tend to only try to
cool it 20+ F.
As for solar, my primary observation would be that
where ever I've lived, when it's cold, the sun usually isn't
out all that long and it's coldest when there is absolutely
no sun.
All of this of course depends upon your local conditions.
One big help is if you have some body of water you can
use as a sink which neither gets very cold, nor ever gets
very hot. A large stream or lake comes to mind. Water
never gets much below 40 nor above 90. Alternately if you
live in some extremely mild climate where the max variation
is similar, and the sun shines regularly, you could probably
do quite well.
