If a mophead type - Hydrangea macrophylla - it can be cut back hard without issue. You do want to wait until spring, when you see the new growth beginning to form and prune back at that time. 4" is a little severe IMO - I might opt for around 6" or so. And remove any wod that doe NOT develop new growth - this can be taken back right to the base of the plant.

You will miss the flowering cycle for at least the first season after the heavy pruning but you should be rewarded with some vigorous new growth that will improve on that bareness and the plant should bloom on schedule in subsequent years. If this is a paniculata or other hydrangea that blooms on new growth, the heavy pruning will not affect flowering provided it is done in early spring.

If in zone 6 or below, you will want to offer winter protection to ensure blooming on any macrophylla.

Thank you, gardengal48 - that's exactly what I wanted to know... it is indeed a mophead, so I will prune it no shorter than 6" in the spring, as you suggest. I'm in Suffolk County, Long Island, which is zone 7a I believe.... given what we went through last year during superstorm sandy, I'm amazed any of our shrubs survived, so we are taking special precautions this year just in case. My hydrangea did take a beating, so we want to give it extra TLC from here on. Thanks again for the help, I really appreciate it!