The best window for structural trimming on most Houston-area hardwoods is late winter into very early spring, before the new growth pushes. The tree is dormant, the cuts seal fast once it wakes up, and you can actually see the branch structure you are trying to correct without a full canopy hiding it.
Oaks get one extra rule: avoid pruning live oaks during the warm months when oak wilt is moving, and if a cut has to happen then, it gets sealed. That is not a preference, it is the difference between a routine trim and losing a mature tree that took forty years to grow.
Deadwood is the exception to every seasonal rule. A dead limb over your roof, driveway, or your neighbor's fence should come off the week you notice it, in whatever month that is. Same for anything broken, hanging, or rubbing shingles. Storm-season clearance work runs all summer for exactly this reason.
Crepe myrtles are where most Houston yards go wrong. Cutting them back to knuckled stumps every winter is not pruning, it is damage that the tree spends the next season recovering from, and it produces the weak whippy growth that flops over the first time it rains on a bloom. Thin out the crossing interior branches, take the suckers off the base, and leave the structure alone.
The honest answer for a lot of trees is that this year they need nothing. When we walk a property we will say which trees are worth touching now, which can wait a season, and which are fine as they are. Quoting four trees when two need work is a good way to sell one job and never get called again.