What can be in an unheated greenhouse?

I've never had a greenhouse before and don't really know what can be out there at different times of the year. However, my dining room table (by south facing french doors) can't take any more seedlings so I could really do with moving things either to the greenhouse or outside as soon as possible. My dining room has the heating turned off, but does get warm during the day because of the big windows.

I have:

Onions (Red Baron, Ailsa Craig, Welsh Bunching)
Leeks (not many - had rubbish germination)
Cabbages
Lettuce/salad mixes (have a container of salad in the greenhouse now, but that was started out there)
Tomatoes
Sweetpeas 
Cauliflowers
Artichokes
Allium (yes, singular - I didn't do well with these!)
Zinnias
Tomatillos
Cucumber
Watermelon
Lemongrass
Radishes
Mustard
Kohlrabi
Chillies
Aubergines

I'm thinking definitely not the chillies, tomatoes, cucumbers, watermelons, or aubergines.

Moving the onions would free up the most space. What do you all think?