I can imagine Basil not liking the cold. Never really cold here though so don't really know for sure, but I would have thought Rosemary was more hardy?

Did you know that Rosemary will grow from a cutting really easily? I just chop off bits of herbs and put them in water in a little old tea pot on a ledge in my kitchen window where the sun can shine in on them. Before I know it they've got roots. Looks cute too! I usually stick something out the spout. Oregano does well in the spout. Curls all around the place.

I know it's a totally different climate here so no idea how that would work there.

Maybe you could also place some of the herbs in pots/with potting mix against a window where there is light as one would do with violets. Then you will have them ready to go as the cold weather disappears.