They go through and remove damaged trees near the easements of the highway lines, as well as branches that could break into lines.
As an aside we lived on the same section of grid as the sheriff, and our power was rock solid for a few years, then he left office and now our power is better than average (at least better than our neighbors who's power line cones from the other direction).
Residential distribution voltage varies by utility but it’s usually in the medium voltage range, 5kV to 35kV, with 13.8kV being common.