Saving a hydrangea from winter damage
Hydrangeas were particularly damaged by this past severe winter. But yours is showing life! Yes, do cut back all of the dead branches to where they are putting out leafy growth. If your hydrangea is a mophead (Macrophylla), which develop buds on last year's growth, you will not have bloom this year, but it will bloom next year. If however, it is an oak leaf type (Quercifolia), it stands a good chance of blooming this year.