Hello, sm. Panicle-shaped blooms suggest that you have very winter hardy (Zone 3) hydrangea paniculatas. These develop invisible flower buds in mid to late Spring and then the buds open in the Summer.

It is not necessary to prune hydrangeas if they are planted in a location where they can attain the size in the plant label (you may not have that). Some paniculatas get quite large and even become small trees while others stay much smaller (say, around 3' or maybe a little taller).

If you have any dead wood by the end of May (the stem has not leafed out), the stems can be cut all the way down.

Hope you enjoy your new home!

I'd wait until end of winter.

I'm thinking maybe little lime hy... Can be pruned back in April to 18"/2'

There are more than one type of hydrangea showing in those photos :-) The top looks like the rounded heads common to H. arborescens (Annabelle type).......I'd be surprised if a mopheaded bigleaf hydrangea would that prolific in MN. And the others do indeed look like a type of paniculata but it is only just wild guesswork to attempt to nail down a cultivar at this point in time!!

But both types are very cold hardy, bloom on new growth and can be safely cut back to a desired size in early spring without affecting the blooms.

I am with GG48 that the first photos are Annabelle or similar H. arborescens and the last ones are Limelight or similar H. paniculata. If you like the look of the dried blossoms your can leave them, but if you don't you can remove them now.

You can prune either or both in early spring before the leaves emerge, but it isn't needed unless there has been winter damage or you want to shorten them (though both will regrow to full size quickly.) IME Annabelle likes to spread via underground roots, so periodically I dig up chunks around the outside of the clump to keep it in bounds. This isn't an issue with H. paniculata cultivars.