Does it grow on old or on old & new wood: Well, you are about to find out this summer. It probably tried to bloom from old wood in early Spring but, the stem got zapped by cold temperatures. Mid to late summer is when remontant hydrangeas will produce blooms from new wood.
Because you are in Zone 4 and the stems got zapped, you most likely have a macrophylla or serrata type of hydrangea. They usually have their stems zapped by ole man winter if you do not winter protect. The others are more winter hardy and thus they tend to be able to leaf out from last year's stems.
To see if the stems are dead or not, you can do a scratch test (very lightly scratch to see if you see "green" or not) or you can wait until the end of May to see if it produces any leaves. By the end of May, the chances are close to nil that it will leaf out. But... you can do the scratch test now or at the end of May.
If you get nothing by the end of the month, you can prune the dried out stems all the way down.
Did you do something wrong by cutting off the old blooms too late? No, there is no such as deadheading the blooms too late. But deadheading is not the same as pruning. Last year's blooms can be deadheaded at any time or never. Just cut the little string that connects the stem to the bloom (it is called a pedicel).
The leaves look a little crinkly perhaps because of late frosts. You have chances of late frosts all May long. Your average date of last frost goes through the last week of May. Expect to need to protect the plant if there are warnings until the end of May ... and since it is an average, assume end of May + two more weeks to play it safe. the more mulch you pu, the more protection the leaves get (the roots are normally not affected by frost so all we are doing with mulch is to completely cover the plant to protect the leaves). You can use frost cloth to protect. Since it still so small, you can also cover it with a lot of mulch when you hear of late frosts. then reuse the mulch elsewhere after frosty times are over. If a frost zaps the leaves, you will get new ones but it will take 2-4 weeks, So if they are zapped, just give the plant water to keep the soil as evenly moist as you can. Then once you are beyond your average date of last frost, you can apply fertilizer. A 1/2 to 1 cup of cottonseed meal, organic compost or composted manure will do. You can also use a general purpose, slow release, chemical fertilizer with a NPK Ratio of around 10-10-10.