Frost damaged cuttings

I'm pretty new to propagating. Last September I started something Okinawa spinach, and longevity spinach.  They did very well. I brought them in for the winter and they continued to grow. A few weeks ago I put them in my little greenhouse that isn't heated. Last week we had temp in the low 30's, high 20's.  This is very unusual for us this time of year. I knew it was forecasted, and re-covered the outside stuff, but totally forgot the stuff in the greenhouse.  Most of the leaves died. There's some new growth at the bottom of the cuttings. A couple have green ok looking leaves on top. So I'm wondering if I should cut the stem of the ones that are low growing.  Should I remove all of the dead leaves of the others.  I feel like if I do the right thing, they will recover, I'm just not sure what that is.  Thanks.

I had the exact same problem in my greenhouse with Okinawa and longevity spinach. I usually throw a blanket on the when it gets cold but I forgot. Anyway, you can cut off the dead damaged parts but don’t cut into any living tissue. The main thing is to not over water them. Put them in a separate section of your greenhouse so you can make sure you dont accidentally over water them. Make sure to keep the soil only slightly damp. Without many leaves the plants have no way of getting rid of excess water and will rot if provided even a little too much water. Good luck!

Thanks you Thomas, will do.  

If you are seeing new growth then the cutting may survive.

Like Thomas said, covering the cuttings with a sheet might have helped them.

Hopefully we are headed for spring and will not have any more freezing weather.

Yes most of them already have new growth at the bottom. Both these plants are very easy to propagate, easy to start, easy to grow.
I did cover the outside stuff, just completely forgot the greenhouse.  I'm in the process of building a new greenhouse, and the one I'm using is kind of sad, so if my brain had been working, I probably would have just bought everything in for that week.  Oh well, it could have been worse.
This experience has made me consider a small low wattage heater with the adapter that automatically turns itself on at a certain temperature.   It won't be easy to get power to the greenhouse, but probably worth it when cold temps hit. Also I have read about putting plastic bottles painted black and filled with water as a no power way to keep the greenhouse from freezing.  I will definitely give this one a try, because why not.  Thanks for your help and support.