we have a second floor sunroom on our summer house that the previous owners made 4 seasons, over open space. part of the problem is that it also only has electric heat instead of the forced hot air of the rest of the house. we've insulated it during the process of replacing a roof and also from underneath but wow is that room cold in winter, we just leave the door closed and use it again in spring. this is in RI.

So if you had forced air going into that part would it be warm?

well it would be a bit cheaper, i expect.

will your newly enclosed space have a door to your other space, or are you opening up a connecting wall completely? if you will have some beefy non-window walls and lots of insulation i dont see why it couldnt work.

Your building permit office will be very helpful about the requirements that they have for heating and cooling occupied space. Not doing anything isn't an option. Not building it to the same standards as the rest of the home will be problematic on several fronts.