Mary, I would wait until the weather is reliably warm and then reassess.

If you cut then off now you run the risk of prematurely forcing more new growth and killing the plants, especially after already losing one set of usable leaves. What is on them now will also help to protect the core that new leaves come from.

If the scraggly leaves turn yellow later they are dead anyway and can be carefully cut off avoiding the middle new growth, but it is almost always better to let the plant decide when, as plants can often pull back nutrition from failing leaves that will help new growth.

If, after it is reliably warm, you see that the plants are putting all their energy into preserving the maimed leaves, you could gently try removing the worst of them gradually. If these are young plants that you just planted in the last few years, you don't want to kill them.

Instead of full removal, maimed or yellowing leaves can be gathered behind the plant to at least partially hide them, as some do with bulbs. They can be held back with a tiny rubber band (as is used for braids) or a twisty.
This is usually better for the plant, as long as it does not cause such a high moisture level near the core to make the growing core rot. That is dependent on the weather and will require your best judgement.

Eirbren, Thanks so much for the information. I really appreciate your help.