Wait and see if it blooms during the summer. Some H. macrophyllas are rebloomers and will bloom on the new growth as well as any surviving old growth. Others will only bloom on last season's branches, so if they are killed back by winter or late spring frosts, then they are just leafy all season, and would need either favorable weather, a hit or miss situation, or as nicholsworth said, winter protection. Yes, cut off the old branches - by now it is clear they won't leaf out.

Depending how close you are to the lake, you may have the advantage of the temperature mitigation that the lake provides. I grew up just a couple miles from L. Erie and we usually had less extreme temperatures than friends across town.

Normally, you could also winter protect it in the Fall so the dead looking sticks survive winter and the up-down temps & produce bloomage earlier but the plant looks to be in a bed with a utility pole and... it might be a pain to put chicken wire around the bush.

luis: It is in a bed, with I'm guessing a transformer or something like that:

To be honest, given how big a hydrangea can get, I'm a little surprised it was planted in that bed, what with the transformer and the peony bush surrounding it.

NHBabs: I'm about an hour south of the lake. I was living in east Cleveland last year, and between there and here, the winter seems a bit milder down here. Tho I'm told this past winter was nothing, so... (I'm a transplant from Southern California.)

nicholsworth: Macrophylla, then. Thank you, I'll look that up and see what I can learn about it. :)

It could be a dwarf or semi-dwarf. By the looks of the old canes it will only grow that tall in one season and maybe only slightly larger the following season if they aren't fully killed back.

And yes that is likely a transformer cover if you are on a street that has buried electrical lines.

A year ago the winter in Cleveland was unusually cold, so much so that Lake Erie froze pretty completely which usually doesn't happen. My mom, who can see the lake from her apartment, said it got to -11, very unusual for Cleveland, since it often doesn't get below 0 at all. Last winter was unusually mild, so you will have to wait to judge if your area now is warmer - I kind of doubt it. Regardless, it must be a shock to be where you are now from CA!

I would seriously consider making that bed larger (or remove entirely), though it will need to be done with caution due to the utility box. Digsafe can come mark where lines are for you. I'd be inclined to remove the hydrangea - if you want to keep it for planting elsewhere, you will probably want to start a cutting instead of trying to dig it up due to the utilities, and then just kill the current one. I also think using something like a fake rock to cover the utility box would be better than having plants that close.