National forests are dog friendly. Most allow dogs on trails unless specifically posted otherwise.
National parks pretty much all limit dogs to paved roads and campgrounds.
State parks likely vary. I know California state parks limit dogs to campgrounds and paved roads - but at some locations, the rangers ignore those limitations.
For me, if I take my dogs with me, I want them to be able to enjoy the outdoors also. But then, I've encouraged my dogs to get outside and play, rather than stay inside playing video games all day...
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