Certified GKH Gardening Expert
It really depends on the variety and how cold your winters get. Most varieties of blackberry are hardy in USDA zones 5-10, which covers a lot of gardens. If your zone is colder, or if your particular blackberries are less hardy, then it's a good idea to give them some extra protection.
If your blackberries are the trailing kind that have to be held up with stakes, remove the stakes, lay the canes along the ground, and cover them thickly with mulch. If the canes stay upright on their own, just mulch around the bottoms. You can protect the upright canes further by putting up a windbreak.
You can read more about winterizing blackberry bushes in this article: https://www.gardeningknowhow.com/edible/fruits/blackberries/blackberry-bushes-in-winter.htm