Hello Pat,

FYI - I identified all images of your plant as a Bigleaf hydrangea (Hydrangea macrophylla). The Endless Summer Mophead Hydrangea is a reblooming bigleaf hydrangea that produces large, colorful mophead flowers on both old and new wood, offering continuous blooms from early summer through fall.

What you describe is very consistent with winter bud injury and/or a late spring freeze event, especially for bigleaf hydrangea (Hydrangea macrophylla) in northern Michigan.
The clues are:
Lots of dead stems ("sticks") this spring.
Most blooms occurred on surviving old wood.
Flowers were on very short stems rather than vigorous new growth.
You spent considerable time removing winter-killed wood.

Bigleaf hydrangeas form next year's flower buds on the previous season's stems ("old wood"). If those buds or stems are damaged during winter or by late freezes, the plant may leaf out from lower buds or the crown, but flowering is greatly reduced. Extension sources note that cold winters, drying winds, freeze-thaw cycles, and late spring frosts are
among the most common causes of bloom loss in H. macrophylla.

More information at the links below:

Hydrangea macrophylla flower buds in winter - Ask Extension

Pruning Hydrangeas [fact sheet] | Extension

Hydrangea: Failure to bloom | Hortsense | Washington State University

Could the late snow have caused it?

Possibly, but the snow itself was probably not the issue.
What often causes damage is:
Warm spell → buds start swelling
Late freeze or hard frost afterward
Flower buds are killed

A late snowfall can actually be somewhat protective if it insulates the buds. The concern is usually the cold temperatures accompanying or following the event. Extension sources specifically identify late spring frosts as a common reason bigleaf hydrangeas fail to bloom.
More information at the links below:

Hydrangea: Failure to bloom | Hortsense | Washington State University

Hydrangea macrophylla flower buds in winter - Ask Extension

Other common causes of poor flowering

In order of likelihood for your situation:

1. Winter injury (most likely)
Leelanau County sits in a challenging climate for traditional macrophylla hydrangeas. The roots are generally hardy, but the exposed flower buds are much less hardy and often suffer winter injury

2. Late spring freeze
Even if buds survive winter, a hard frost after bud swell can eliminate the flower display for the season.

3. Pruning at the wrong time
It doesn't sound like you did this, but if old-wood hydrangeas are pruned in fall, winter, or early spring before growth is assessed, many flower buds can be removed

4. Increasing shade

If surrounding trees have matured since 2018, flowering can gradually decline. Bigleaf hydrangeas usually perform best with morning sun and afternoon shade. Too much shade reduces blooming.

5. Excess nitrogen
High-nitrogen fertilizer can produce lush foliage at the expense of flowers, though it would not explain the dead canes you observed.

6. Deer browsing
Deer often remove terminal buds, which are exactly where many flowers would form.

What should you do with the dead sticks still in the plants?
Yes.
For bigleaf hydrangeas, the recommended approach is to wait until growth is well underway in spring, then remove stems that show no living buds or green tissue. Entirely dead stems can be cut all the way to the base. Stems that are alive should be retained because they may carry flower buds.

A simple test:
Scratch the bark lightly with your thumbnail.
Green underneath = alive.
Brown and dry all the way down = dead.
At this point in the season, any canes that remained completely bare while the rest of the plant leafed out are safe to remove.

Looking ahead to next year
For Leelanau County, I'd suggest:
Leave stems standing through winter.
Apply 3 to 4 inches of mulch around the root zone.
If these are valuable plants, consider a wire cage filled with shredded leaves after dormancy.
Avoid fall pruning.
Leave spring cleanup until you can clearly see which buds survived.

Check out these articles from the University of New Hampshire and Penn State University at the links below:

How do I protect my ENDLESS SUMMER Hydrangea over the winter? | Extension

Why Doesn't My Hydrangea Bloom? 

I hope this helps!