Perennial hibiscus -- those dying back to the ground each year, as opposed to woody types like Rose-of-Sharon -- can be cut back any time after the stems have died, but generally are pruned in late winter or early spring (roughly March). For native species, it's helpful to overwintering insects to leave the stems on even longer, in case any solitary bees are using the hollow stem centers as shelter and haven't yet emerged for the year. It won't impact how well and when new growth emerges out of the base of the plant.

Hydrangea pruning depends greatly on the type of hydrangea, as they don't all flower in the same way. Our Pruning Hydrangeas page goes into more detail, and the type in your photo appears to be "bigleaf" hydrangea (Hydrangea macrophylla), and as such, is not pruned between now and after its first flowers fade next year. Resist pruning even if stems look dead during winter, because these hold next year's flower buds; if removed, they will not grow back. While some varieties of bigleaf hydrangea can produce new blooms on new wood, and therefore have some forgiveness for mistimed pruning, without knowing the cultivar being grown, we can't say if that's the case here. (Even in that situation, pruning in fall, winter, or spring would still remove the first batch of flowers.) In late spring, if new growth is fully emerged and a few stems are still leafless, then those individual stems can be trimmed back.

Miri