Some riffs:

(A.) I planned on pruning these Hydrangea late in the spring. Yes - textbook, you prune them in "late summer after flowering" as they flower on old wood...but...I think that idea must come from the practice where you are just blindly cutting the plant back? As if, you cut the plant back hard "after if flowers," late in the summer, and this gives the plant enough time to push out some new growth before the season ends, on which of course, there will have formed flower buds for the next season.
But this is Buffalo, NY and the traditional, old-school Hydrangea macrophylla doesn't often have its primary flower buds survive the winter. More often than not the flower buds are killed off by winter and early spring cold.
AND...I don't know about you, but I think we appreciate the form and color of the faded Hydrangea flowers well into the fall and early winter...so we don't cut them back, we don't deadhead.
Furthermore...I believe a good portion of the macrophylla offered in the nursery trade locally are what we would call "rebloomers" - these contemporary cultivars put out flower buds on both old and new wood and therefore, if the buds on old wood are killed off over the winter the Hydrangea still will flower later in the year on new wood.

(B.) So...I'm pruning now (this morning), in late winter/early spring. I am not cutting back or reducing the plant in size, I'm essentially just cleaning. These Hydrangea get filled with deadwood pretty quickly. And, seemingly, as a rule, anytime anyone does prune them, they just top branches (I suspect in late summer!) about 8" off the ground and it leaves behind this mat of dead stubs that clutters the base. When cleaning up in the springtime - since we don't deadhead -  the flowers from last season need to get cleaned up ("need" meaning, for visual reasons; for order) - and often the snow and perils of winter have broken a good portion of the branches still holding on to last seasons flowers...

(C.) - I suppose it possible, at times with MATURE plants, a good hard rejuvenation prune - in late summer - may be helpful to give them a fresh start and a reason to vigor (not really a verb...but...).

Method
This was a sizable project (today's: depicted in images above) taking about 90 minutes in deep focus to prune this cluster of 7 plants. In this garden, there are still another 20 to 25 macrophylla to prune. I performed the work with earplugs in, something I like to do so as to keep me in a meditative space. I need standard hand pruners only,. I've been using Coronas this season, not Felcos. $24 a pair vs $60 and the same cut as far as I can tell. I go through 2 or 3 pair a season, so, it's relevant.
I start at the tips closest to me combing through one branch at a time. If it has a old flower, I cut it off to the next bud. Many branches won't have a flower but a large pointed terminal bud. Chances are its cooked from the winter, but you can't really tell for sure, so I leave it. Any breaks I take back to the highest bud. I go down each branch and eliminate the dead laterals. I get down to the ground and I clear out all those dead stubs and the number of full length dead branches. For the most part, this is it, just deadwooding, but every so often there is a crossing branch I take out or "other things" that I don't like - but this is very minimal.

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Today.
Weeping Mulberry doesn't seem to find its potential around this region but, elsewhere, I see it as a well pruned winter sculpture.

I have a couple that I am able to work with but there is always a "conflict" with the client - they can't help but take trimmers and pruners to it and hack it back during the summer months when it grows super fast. The aggressive and control oriented pruning always leads to the heavy production of buds and shoots; 18 months later the tree is a mess.

With the two I worked with today...we are starting with one of those messes.

Method:
One can't cut at a Mulberry heavily - it will just cause a violent bud/shoot reaction. At the same time, we're starting with a mess - there are 1 to 2 inch branches crossing each other throughout the body of the crown. So, I allow myself two to three "big cuts" on each tree but keep them deep in the interior where they MAY be less likely to push buds (my speculation as there is little sun in there and everything on the inside is already dead) and only one "big cut" on either of the major skeletal branches. We'll deal with the fallout from this, if there is any, later. After these big cuts, I only cut out deadwood.

End Note:
Every pruning job like this, regardless of the species, is moves based on speculation of how you think the plant/tree will react - it's an art, but it may be best to use the term "informed practice" before we turn loose someone's creativity.