Dahlias will not survive a hard freeze. If you want to preserve them, you'll have to dig them up and store them overwinter. Store them in a cool, dark, place.

Good idea to cover them with dry sand or dry compost, and put them somewhere frost free and out of the way of mice!

it also depends how deeply planted they are. I had several that were 6-10" deep and they came up for years with typical winter cold but the harsh winters of 2010/11 and 11/12 did for them.
the others I list and store frost free in the dark.