Physical Danger
Have you ever been out in nature? If you have, you've probably faced the many dangers out there in the wild world. If you haven't, you should definitely consider another line of work. You can be hurt by a lot of things in America's state parks and wildlife refuges: snakes, bears, alligators, venomous plants, the sun, wild boars, bugs (so many bugs), rainstorms, mudslides…basically everything.
And that's just the natural danger part. Remember that line from Jurassic Park, where Samuel L. Jackson says that they have all the problems of a major theme park and a major zoo? Being a game warden is kind of like that, except the theme park is filled with trapped kayakers, wildlife poachers, and occasionally even drug dealers (but thankfully, no dinosaurs).
You'll have search and rescue missions and even homicide investigations. There's a reason you carry a firearm, and you'll be trained against the same dangers as any other law enforcement officer. As the story of Guy Bradley teaches us, the most dangerous part of being a game warden may still be other humans.
Point is, the name of your job is public safety. This starts with you, so make sure that if you want to pursue this line of work, you are up for all the risks Mother Nature might throw at you.