Cut down all of the old vines, they are dead. You will probably have some new plants start growing in late May early June - from seeds from last year's plants.

Morning glories are annuals and won't come back from old plants, so go ahead and get rid of the old vines. Some people have had some varieties sprout from self-sown seed, some haven't. I never had them come up from self-sown seed (I mainly grew the common variety, Heavenly Blue). And be sure to distinguish morning glories from bindweed, which is a bear to get rid of and WILL come up everywhere and twine around all your other plants! If you want to err on the side of caution, start some again -- or just wait and see what happens!

Before you take them down check for any seeds!!!

LOL.

Especially if any of them are rare or different varieties you can probably get some trade for them and you can sow them and get your MG again this year.

I had beautiful morning glories in a home once that came back from self sowing year after year after year. I never had to plant them after that first initial planting.
I always removed the old vines after I was sure they were done sowing their seeds.
I long for that old house sometimes. I don't have morning glories in my new house yet and I really miss them.