Hello, Travis. Hydrangeas and vibirnums (especially the vibirnum snowflake) can be confusing. However, in general, vibirnums flower very early compared to hydrangeas. VS is currently in bloom here while hydrangeas are just waking up from their slumber.
The first photo appears to have panicle shaped leftover blooms. This suggests the shrub may be a Hydrangea paniculata or H. quercifolia (also known as oakleaf hydrangea). Oakleaf hydrangea is easily recognizable and distinctive from a paniculata because the leaves are larger and shaped like oak leaves. If it is one of those two hydrangeas, it should bloom much later, in July perhaps (not sure where you are located?).
You can leave these dried out blooms "on" and let them fall on their own or cut the little string that connects the bloom to the stem. That is called deadheading, not pruning. Do not cut the stem though. Hydrangeas develop invisible flower buds usually at the end of the stems at different times of the year. Some have already done so be careful pruning stems or you will loose 2015 bloomage. So, without knowing for sure which plant you have, I would err on the side of caution until you find out FOR SURE.
The second picture was more difficult. I could not tell from the dried out blooms what it is. I speculated but could not decide. Maybe this is the vibirnum??? A photo of the bushes in bloom would help greatly. And information about when the blooms open.
In general, there is usually no need to prune hydrangeas so you could skip pruning the majority of the time. Provided that they are planted where they can attain they advertised size at maturity, you normally just leave them alone or do light pruning such as removing stems that cross or that are dead.
But right now, it is impossible to know which ones are dried out dead from the picture. Observe when they leaf out and then remove any stems that fail to leaf out. Rejuvenation pruning is a form of pruning sometimes done on older Hydrangea macrophylla bushes (called mopheads and lacecaps) when they get very large and when they bloom sparingly or smaller than before. But your shrubs are too small to need that.
In either case (hydrangea versus vibirnum), cut crossing stems and leave them alone, check in a month (?) when they have leafed out and then prune any stems that failed to leaf out.
The following hydrangeas develop invisible flower buds in July-August: H. macrophylla (referred to as mopheads or lacecaps), H. serrata (smaller than H. macrophylla with serrated leaves) and H. quercifolia (oakleaf hydrangea). These should be pruned after they bloom or no later than the end of June.
The following hydrangeas develop invisible flower buds 1-2 months after they leaf out in Spring: H. paniculata (panicle shaped blooms and small leaves compared to others) and H. arborescens (the best known one is called Annabelle).
If you live in the northwest side of the country, there is one more type called H. aspera that is common over there and has leaves with fuzz/hairs that grows on the leaves; it develops lacecap blooms most of the time but there is one known variety whose blooms are mophead like. These u s u a l l y get large 10' by 10'.
Visit this website with lots of hydrangea information, including a page that helps identify the common hydrangea varieties (yes, pictures included):
Regarding vibirnums, you also need to prune lightly, usually best to do that after they have bloomed but before they set seed if the variety sets seed. You can also pinch the stem endings to get a fuller bush. I have left some large ones in the yard alone (ie, no pruning) and shaped them into a tree shape. They must be 12' or taller by now. Here is more info:
https://www.gardeningknowhow.com/ornamen ... runing.htm
Does this help?