With the asparagus as tiny as you describe, I think it would be unwise
to move them from a 50-90 degree environment to one that could go below
freezing. Going from 90 to below freezing is a bit much for seedlings. I
would probably choose the 50 degree room for a transition. Is there any
way that you could rig up a light for them in that room (any light, even
if not a "plant light")?
With cabbages growing that large, I'd probably re-pot them if they must
stay in the greenhouse a few more weeks. If you do, they should be just
fine.