Cars aren't the main problem really. An overpopulation of deer puts a strain on the local ecosystem that nature cannot cope with. A given area of vegetation can support a given amount of herbivores, whose population is naturally checked to near the given amount by predators. Since humans 'meddled' by killing of top predators, there are now more deer across most of the U.S. than the vegetation can support. Unchecked, the deer would strip the vegetation, causing long term ecosystem damage. Also, less food means weaker deer, who would be less likely to survive the winter. Due to the 'meddling' humans took the place of the top predator, and should we stop checking the herbivore population, ecosystems would be changed drastically as vegetation and deer populations plummet.
They even strip the bark from young trees here in winter. Lots more coyotes/hybrids here now too despite it being open season on them year round. And while not the primary problem, everyone I know has had collisions with deer here. There are just too many. They dart out of woods right into traffic. On country roads, attentive and slow driving with your hand on the horn can help. But they often cross busy highways with predictable results.