Most herbs do not do well indoors unless you have very bright light. And mason jars are a terrible container for them. Do the jars have drainage holes? If not your herbs need to be moved into proper plant pots if you can't put them in the ground. All the ones you name are fully hardy perennials, except basil, and would be much happier outside. Basil is a tender annual and can be kept inside temporarily if you have sufficient bright light. I don't really understand 'closing up' your garden. Don't you grow any overwintering crops?

The garden is run by the town I live in-it’s only open from April 1-Oct 30. They then till all the plots and lock the gates. We stay fairly chilly but mild here from Nov until after the holidays, but I live just outside Washington DC close to the mountains, we get decent snowstorms and below freezing for much of Jan-Feb. I’ll replant them this week into plastic pots and keep them outside as long as I can. I understand from doing more research that the basil will probably not make it due to its annual status anyway. I am in “negotiations“ with my spouse about a raised garden bed in the backyard next spring, if I can keep the rest of the herbs alive until then, I can put them in the ground. Thanks for any and all advice!!

The basil might have the best chance inside in a sunny window. It will not get enough light and I do not expect it to thrive. But we can always hope that it will beat the odds. For all the rest, pots outside sound best.

That's bad luck about the garden. And a terrible waste. Here the plots are open all year round and once you've got one you have it as long as you keep up the rent. There's a lot of stuff you could have survive through the winter.

But if you have a backyard I'm sure you can find a space for your herbs. Do you have any flower beds you could tuck them into? They don't need a special raised bed. But keep the mint in a pot. If you use a lot of herbs it's a no brainier to grow your own.

I'm in WV, 6A, in my own garden, and temps have gotten to 19 degrees. But I just harvested lettuce from under a little plastic tent, and I still have collards, kale and savoy cabbages under row covers. Such a waste to close up a garden Oct. 1. It's even too early to plant garlic!

Perhaps you can persuade the garden board to keep it open all winter. In your zone, April 1 is too late to sow some vegetables--peas and spinach for example.