We would need to know what type hydrangea. If you are attempting to grow the big leaf types (macrophylla) they are going to need winter protection measures in your zone. The macrophyllas bloom on buds set the previous year, or 'old wood', and while the plants themselves would be hardy and come back from the roots, the flower buds wouldn't survive your temperatures. There are some newer macrophylla hydrangeas bred to bloom on both old and new wood - with those, you would lose the first round of flowers but still have the later flower heads that would form on current years growth.

If you are not interested in protecting in winter: http://www.endlesssummerblooms.com/the-collection

Other types of hydrangeas that could do well for you without winter protection are hydrangea arborescens (like white Annabelle), hydrangea paniculata (the pee gee types), and hydrangea quercifolia (oak leaf).

When the tag is not a descriptive label, it is difficult to know the exact variety and that usually helps answer the question. If you saw colored round blooms when you bought it then it is probably a Hydrangea macrophylla. In general, hydrangeas are deciduous so they loose the leaves in the winter months (although I have one oakleaf hydrangea that was not in the mood to do that this year). H. macrophylla develops invisible flower buds in July-August and these open in your Spring. However, they are usually hardy to Zone 6 only (a few to Zone 7). In colder zones like yours, the stems (where the flower buds are) dry out and die. The plants roots are usually ok though so they generate growth from the crown or base again. However, these new stems will not develop flower buds until July-August (unless this variety is one that reblooms but that is rare). To prevent loosing the stems and the flower buds, try winter protection. Do a search on the forum for the phrase 'winter protection' for additional information. The concept is to somehow protect the sides and top of the plant by filling the area with mulch or leaves in the Fall (when the plant goes dormant and before extremely cold temps will damage the invisible flower buds. A piece of cardboard on top with rocks makes sure that the mulch does not fly away and some chicken wire around the bush helps with that too.

It is probably too late to protect now. Wait to prune the dead looking sticks until sometime in May as they will leaf out late sometimes. If they do not leaf out by mid-May then assume there probably will not be flower buds and the stems died out. You can prune those at ground level.

A rebloomer variety of H. Macrophyllas -such as the Endless Summer Series, the Let's Dance Series, the Forever Series- will suffer from dieback but the new stems will generate blooms (albeit later than normal, probably in June-July) since you have to let the stems grow a little so they generate flower buds and bloom.

Another alternative is to grow them in pots and bring them inside into a garage or shed when the plant goes dormant. Just do not forget to water it once every week or once every two weeks.

Yet anbother alternative would be to use hydrangea varieties that are more hardy. In Zone 5, you can try: oakleaf hydrangeas (the leaves look like oak leaves and the leaves also look very nice in the Fall), paniculatas (they have panicle shaped blooms) and arborescens (also called the smooth or wild hydrangea, arborescens is a hydrangea native to the US and is best known by the Annabelle Hydrangea and its newer "versions").

I hope this helps,
Luis