It is not optimal of course but those seedlings might survive.
They are all semi-hardy. What you could do is make a tent or hoop house (plant a tomato cage on the ground, put buckets of water and the seedlings under it, cover with clear plastic, secure to the ground with bricks) and leave them there unless it really freezes.

Next year, make yourself a cold frame, and the semi-hardy seedlings will never give you a problem again. I make a hoophouse, well secured, plenty of buckets inside, precisely to get seedling out of the house ASAP. You are hardly the only one with space problems in the spring.

And be sure to make a note of your starting date this year in your journal so that next year you'll remember to wait a couple of weeks longer on semi-hardies. ;)

On the hardening off - in and out and in and out for a day or so is fine but much longer and it just defeats the purpose of hardening off so it's best to either wait until they can safely remain out all the time after the first day or so or build your self some sort of sheltered/protected place for them outside. Under a porch, near the house foundation, out of the wind and direct sun, etc. Might also want to consider plastic cloches out of pop bottles or milk jugs if all else fails.

Good luck with the seedlings.

Dave

Have you had those seedlongs grown outside, they woulh have survived without worry.
temps down to 20F(night low). So if you want to plant them in the garden, should harden them up. For example, leave them outside till 8PM, bring them in to garage.
Next night leave them outside longer,...longer... longer
When your night lows are over 30F, you can transplant them.
Oncethey get used to cold and grow just a bit, then don't worry about frost or light freez.

I have planted cabbages in the fall and they overwintered.
We have had many nights with lows going down to 15F. So your task is hardening them up.

Here in my zone 6, I'm starting onions today, broccoli and cabbage next week, Peppers the week after that and tomatoes the week after that. But, as soon as the snow is gone, I'll sow in the open garden parsley and spinach. And peas by the middle of the month.

broccoli, cabbage, cauliflower, brussel sprouts, and escarole

Cabbage is usually considered "hardy". The rest are "semi-hardy" so less cold tolerant.

Here onions were started in January and will go to the garden this week. Cabbage was started Valentine's Day and will go to the garden this week. Broccoli, cauliflower and peppers get started this week. Tomatoes get started on March 15th when the broccoli and cauliflower go to the garden.

Dave

When do you guys start Bai Tsai ( Asian Brassicas ) type plants ?