Taking a large dog to New Mexico State Parks
Most state parks allow leashed pets, with a few exceptions.

State park rules
The New Mexico State Parks FAQs says pets are allowed at most state parks, must be on a leash at all times, and are not allowed at Rio Grande Nature Center and Living Desert Zoo & Gardens State Parks. The New Mexico state parks rule 19.5.2 NMAC says visitors must restrain dogs on leashes of no more than 10 feet, prevent excessive barking, and not leave animals unattended in vehicles or campsites. It also bars animals, except service animals, from visitor centers and Smokey Bear Historical Park.
Camping
The New Mexico State Parks camping page repeats the 10-foot leash limit and bars leaving pets unattended in vehicles or campsites.
Rio Grande Nature Center
The Rio Grande Nature Center State Park page says leashed pets are allowed only in the parking area and on the adjacent city trails.
What it says about the dog
Every park rule assumes you can control the dog in public. Ask any provider to prove that control around people, wildlife and other dogs.
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