Well, this isn't really advice, since I asked a simular question, but I have the same green house, and I put my flats with perenials in it as soon as I sowed them. My dianthus are just peaking out of their peat pellets. The H2O in the trays even froze for a while, but they didn't mind.
Cecilia suggested that I use cloches, but I think you still have to harden them off.
Good luck!!

If you can locate some old storm windows , prop them up againt a southern-facing wall and stach plants underneath. i
can start putting perennials and such out immediately. I have had my perennial seedling out on the patio in ols aquariums with glass laid across the top.they made it thru the snow and cold w/o problems. I put them out early MArch. will probably put my delicates out in a couple of weeks once I get my ""cold-frames"" emptied of the lettuce and perennials. If it looks like it is going to get too cold at night, I just drag the tenders in for the night or throw an old canvas tarpover the glass. have been doing this for years now
the only thing I frosted were my loofa seedlings last spring. the plants grew but refused to even form any blossoms
mary
Mary

Just keep in mind that you're just as, if not more, likely to lose seedlings to sun scorch than you are to cold as you move them outdoors. Hardening plants off isn't just about adapting them to the cold, it's about adapting them to direct sun and wind. Pick a still, cloudy day to start moving them out and gradually expose them to more direct sunlight. Watch that little green house on hot days as well -- I'll bet it will bake plants pretty quickly. You should be sure to vent it during the day.

I am planning on hardening off my Tomato seedlings, can I use a window well, which I will have access to from the inside?

Sophia