I'm not sure what advice to give you for where you are, but here in UK we wait until spring and then only cut back those stems which flowered this year and any old wood. If you cut it all back, you will lose next year's flowers.

What kind is it, Laceybaby? H. arborescens seems to be the only kind that can be cut down in fall or winter and still bloom the following summer.

If you live somewhere where there are frosts its best to leave it all until the spring as the dead flower heads give a little protection to next years buds. (if they are mopheads or lacecaps)Then do as Ojibway says, cutting out any stems you don't want such as very spindly ones or very old ones and trim the ones that flowered last year a little way back to a good strong bud. don't do it until after the last frost. Mine always flower well on this treatment. The exception seems to be Annabel, which flowers on the new wood.

No, leave the flowerheads on for a bit of winter protection, and then prune back to the top 2 buds in late march, take out any dead wood, any crossing, or diseased stems, and give a general purpose feed, if you have blue flowering ones, give a feed of aluminium sulphate or sequestrine, if pink and the flowers are beginning to look a little purple, give a feed of ground limestone at 2 ounces per sq yd

Michigan is a pretty cold state, so unless Laceybaby lives right next to the lake, it's unlikely to be a H. macrophylla variety.

What about Hydrangea paniculata varieties though, Tugbrethil - these can be cut down in autumn and still flower the following year. Would it be too cold to do that in Michigan?

Many thanks to all of you who helped with the question.
Laceybaby

Thanks, Bamboo! I haven't dealt with them since I first started gardening, forty-odd years ago. Back then, the conventional wisdom was that if you cut them back anytime after midsummer, they wouldn't bloom the next year. Someone must have known otherwise, but it apparently didn't filter down to the low desert, where they are rarely grown. Their info indicates that they should be hardy enough to work in most of Michigan.