Southern exposure/windows help a lot here. We face south with no obstructions, so get plenty of sun (when its out). Usually about 10am until 3pm the furnace takes a brake on even the coldest/full sunshine days.
If i could design my own house, it would have tiny north facing windows (just for some natural light/ventilation in the summer) and a whole row of south facing glass. With wide enough overhangs, summer sun wouldn't heat it much at all. With enough mass (concrete floors?), you could really store heat for some time.
Watch out for ice damming on your roof. I know when we get too much snow i usually grab the roof rake and take down the first 8 feet or so all around the house (hip roof/ranch...easy reach if i use a short ladder). I never have any damming, but i worry about all that weight sitting up there (i think this 1950s dump should hold!). I can remember years past watching neighbors get up on the roof with shovels and even snowblowers. My hip has very little pitch so it doesn't shed snow very easily. Once these asphalt shingles go to garbage i'm moving to a metal roof and not worry about it again in my lifetime.
Be interesting to run a mini split off a bank of solar panels. I'd run them wide open on those sunny days...get the interior temps up to about 85F
Its free heat at that point. Shut it down until it drops back to about 65F after the sun sets.