When you prune Hydrangea just dead head the flowers and leave the wood alone.
That is only, if that "type" does new growth on last years wood. Not every one does. My Annabells, and I have 3 of them. In about December I will cut the whole plant down to about mid-calf or knee height. The last years dead growth only serves as a cage to help the new growth, whitch comes out of the grown to not fall over too much.
And my Oak Leaf Hydranges, have 2, they are both about 10 feet tall, have not pruned them yet, however, they would servive a couple feet off , they bloom from old wood.
Then there is my Hydrangea TREE. Yes, its a TREE, if I walk inside of it, from the ground comes one single trunk, about 3 foot, from there branches out all sort of limbs. And I said I walk inside it, and stand straight up tall. It's height is level with the height of the house garage roof. My pruning of that is , walkng again---inside, and standing up straight, I am 5 foot 5. I look for dead branches, or branches that are crossing and rubbing on eachother---those I deside which to cut out. The dead I wack them out. It is on the way to bloom now. Very long flower clusters in creamy white.
Then I have one I shipped in from Japan, I never prune that one, it blooms on old wood.
Then I have a wee one, it only grown 4 foot, I might give it a wee shaping, but normally I do not touch it.
All Hydrangeas are not the same. Please no blanket statements.