Big Bend Nat. Park is like all National parks being 'semi' pet friendly. Pets are permitted on leash in the camp grounds, but not on any trails. We were there the week between Christmas and New Years with our dog and cat with no problems. However, there are no campgrounds inside the park with hookups except for a concessionaire operated area of the Rio Grand Village campground and they do not take reservations. They are very full in the summer months because of the need for air conditioning for you and your pets - it gets hot down there! Of the other two campgrounds, one does not permit generators at any time and the third, The Basin' is beautiful but has a 24 ft limit for RVs due to the mountainous terrain.
My recommendation is to stay in Study Butte at the Big Bend Motor Lodge and RV campground as we do for the creature comforts
and use the toad for exploring a very uniquely beautiful National Park. (Do Not miss the Study Butte Mall! <wink>
This is a a very unique area of the State!
Also in that area are Ft. Davis and a very nice State Park with full hookups (rare for Texas State Parks)that is a short drive from the McDonald Observatory - there is nothing quite like a star gazing party at the Observatory! Reservations for FHU sites in the Davis Mountains State Park are highly recommended and should be considered mandatory.
Hope this helps and enjoy your visit to the Great State of Texas!