I live just outside New Orleans, and we normally have very mild winters
This year is a bit of an exception, there have been 2 hard freezes so far, and another coming next week.

I have a heating mat and 2 trays of seeds that have a few seedlings an inch or so, and a few just started breaking the soil. - more to come..
Some peppers and morning glory germinated, but i still have more, and also papaya, and some cactus

They actually get a decent amount of light, at least when its not cloudy.
I have them in a southern window on a small table.

I do have a greenhouse, but the only heat it has is a small wall-mart cheao heater. last night it was about 34 outside, and in the greenhouse i thing it was about 45-50.

i already had 2 seedlings die.
not sure why, i had a few fungus gnats, but not that many, and i sprayed with neem and clove oil.

i do keep my house rather cold, about 60F or so to keep the heating bills down. heat pumps arent very economical

did the pepper seedling die from it being too cold, or maybe the gnats ?
i dont want the soil to dry out too much, i still have seeds yet to germinate, including papaya and cactus, so i lightly spray the top, it dries fast in full sun

also what im worried about is how big they will get, as opposed to how cold it will be in the greenhouse when i try to move them (late feb maybe?)

any ideas ?