Certified GKH Gardening Expert
Depending on your USDA zone, this may not be the time to do so, unless it does not get below freezing in your area.
The Hawthorn can handle pruning during winter, but depending on the type of bramble that it is, it may not be the time to prune. Can you include pictures, and your USDA zone? This will help me to determine the best course of action from here.