Hi, 

These are macrophylla type or Bigleaf Hydrangea. They can either bloom on old wood or if they are a re-blooming variety, they will bloom on old and new wood. If you don't know if they are the re-blooming type, you could wait and prune them after they bloom this year. You can prune dead branches that do not leaf out anytime, though. Macrophylla hydrangeas can often succumb to dieback from cold winters, where they die to the ground and regrow from the roots. That is what looks like happened to some of these branches. You can wait to make sure it is fully leafed out then prune any sparse branches. If you don't receive blooms this year, then it could be from the late frost we had this past week. 

Also if appears that the second shrub or what is in the second photo you submitted, is an Oriental Bittersweet vine that is growing up through it. If you look closely you will notice the leaves are different. That is invasive and you would want to remove it before it takes more the shrub. You can cut it down to the ground and keep cutting it when it sprouts back up or cut it and immediately apply a systemic herbicide to the fresh cut wood. You will want to be careful if you choose to use herbicide so that it doesn't get on the hydrangea. You can use a small sponge brush to dab it onto the cut stems, or carefully spray the wood and shield the hydrangea from any drift with a piece of cardboard. A systemic herbicide with the listed active ingredients of glyphosate or tryclopir is best and avoid anything with dicamba as that can travel in the soil and harm the surrounding shrubs. 

Emily

You're welcome!