Welcome to NGA, Natalya.
Moths that stop by hydrangea arborescens (that includes Annabelle and its "cousins") and deposit their babies will create this problem in May and June. These babies develop into larvae that try to protect themselves from pesticides by covering themselves in this manner and, of course, to eat the leaves.
In small infestations, you can cut the leaves off and squish them with your fingers. But if that rates a 10,000,000 in your eek scale, you can also drop them in the trash or in beer. ;o))
The curling of hydrangea leaves could be caused by one of two insects.
The hydrangea leaftier larva binds two or as many as four leaves together with strands of silk into a cup form and then feeds and rests between them. Pulling apart the leaves will reveal a half-inch-long slender green caterpillar with a black head.
The leafroller insect also causes similar damage, but rolls only one leaf, then feeds and rests within the rolled leaf. Both insects cause unsightly damage, but won't harm the shrubs. When you see the damage in early spring, open the leaves to inspect the contents and squish the buds that you find.
Clean up the ground below the shrubs, too, because the caterpillars drop to the ground and pupate in the summer and emerge as adult moths. Look under the leaves and during the day & night.
If the infestation gets out of control, you may need to spray Bt, Bacillus thuringiensis kurstaki (DiPel, Thuricide, etc). I would suggest -next year- applying it again but earlier than when you first detected the problem this year. The damage is typically cosmetic and it would rarely kill a hydrangea. But they say to "never say never", hu? ;o))
Does that help you, Natalya? Luis