95% of the world's biomass is in the form of beef, pigs, and chickens, and 5% is in the form of wild animals. A regular size feedlot will have 98,000 cows being bulked up with antibiotics in preparation for slaughter. Factory pig farms in the USA commonly have more than 1,000 pigs and they produce an enormous amount of waste that goes into the rivers and lakes and bays. Deer may spread disease (but most of these diseases origninated with cattle and were passed along to deer and bison and moose) and deer may be involvved in traffic accidents with inattentive drivers, but deer are a trivial component in gas emissions driving global warming.
Deer control by hunters has never been effective and I would have to guess that that is intentional. Killing off a male and not a female is a great way to insure that the overall population continues to expand as a single male will impregnate a dozen does.