No real hurry. But I would pull up all plants whose productive days are behind them and toss them in the compost pile. Hopefully harmful pathogens go with them. Rake off old leaves, stems and whatnot. That leaves bare soil... what to do? You can plant a cover crop, but I wouldn't. For me it just prolongs the time I can start planting in Spring, but your mileage may vary. I just toss a load of compost across the empty beds and rake or spade it into the surface. By planting time, the compost is well integrated into the soil. Then I forget about it until next season.

Before we moved to Texas, we lived in upstate NY. Our vegetable garden shut down by the first frost (frost? What is that, asks a Texan) and we put our leaves, well chopped up, on it, after removing remaining plants and putting them on the compost pile. Then in the spring when the snow melted (somewhere around July 1st, as I remember) we tilled in the partially rotted leaves. This amended the soil, kept the garden pretty weed-free until we were ready to plant, and saved the leaves going to the dump. If you don't have leaves, someone near you does, and would be very glad to get rid of them!

It's probably too late where you are, but you might think about some fall/winter things like chard, lettuces, brussel sprouts, broccoli and others for next year.
They have to have some time in the ground while the ground is still warm to start growing, then once they are established, they do fine even in snow! (I don't get snow, so I don't know which ones actually last through it. This is what I've read)