Good luck with your herbs.
Basil dies at the first frost, however, if you have let the plants go to seed and let the seed fall, or cut the branches with the mature seed and just let it work its way into the soil, you will most likely have plants growing in the same place next year. We put the mature seeds in a grocery paper bag before the cold weather and sort out the seeds when we have more time. This is a mild winter climate so we are able to plant seeds and get beautiful plants, however we also buy a pony packI(6 seedlings), so that we have basil earlier.
The sage,mint and oregano will grow back in the spring, at least in a mild winter climate they do. Arugula also grows back. Bay leaf and rosemary stay green all year round,of course. I had a santolina plant in a half barrel in filtered shade and it kept coming back for 3 years, but I tried to move it and it died.
These are the only herbs we use in cooking, but you have made me realize that I really need to get some new ones.
We do have what is called kren (chren?) in Northern Italy, but I don't know if it is really an herb. It is just horse- radish and it's really hard to keep watered enough to keep it alive in the heat. I have no idea what it will do in winter.
L

My Oregano and Sage come back every year, twice as big. Same with Chamomile and Yarrow. I also have tons of Lavender and some rosemary that stay all season (as mentioned in the above post).

I Love the Basil, I can never plant enough, but it always dies and I always start new flats in Feb/March.