As long as the roots didn't freeze it should survive.* You can prune off dead wood at any time.* Here's some info on your bush.
Next time a hard freeze is expected you could either bring it indoors or wrap the pot and the plant with a sheet or blanket.* Don't use plastic as it can cook your plant if you forget to remove the plastic and the sun shines on it.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.