The spider web-looking things you see in trees are not actually made by spiders. They are large webs spun by caterpillars, specifically the fall webworm and the Eastern tent caterpillar.

• Fall webworms create these webs in late summer and fall. They form loose, thin webs mostly at the tips of tree branches. They feed on the leaves inside the web, and while they can defoliate smaller or younger trees, they generally do not cause serious harm to established trees. They feed on a wide range of trees including pecan, persimmon, wild cherry, and others.
• Eastern tent caterpillars spin thicker, cottony webs usually in the crotches or forks of tree branches in spring. Their favored trees include fruit trees like cherry, apple, crabapple, and some other deciduous trees. They are sometimes called spring webworms.

Both caterpillars create these webs as protective nests to live and feed in. Although unsightly, they mostly cause cosmetic damage, though young trees might suffer more leaf loss. The webs can be removed with a broom or pruning, and insecticides targeting the caterpillars can help control them if needed. So what looks like spider webs in your trees is actually the work of these caterpillars making silken nests to feed and develop inside. They are harmless to people and mostly not harmful to mature trees.