If your dog falls under Spain's PPP (potentially dangerous dog) system, the muzzle and leash rule set out in Real Decreto 287/2002 applies everywhere in public, not just in town — a hiking trail, a national park, or a dog beach are all public spaces for this purpose, and the official decree's muzzle-suited-to-the-breed and non-extendable-leash-or-cord-under-two-metres requirement applies on all of them, with no outdoor-recreation exception.
This sits on top of, not instead of, the general rules covered elsewhere in this section: a PPP dog still needs to follow national park leash expectations and any municipal dog-beach rules, but it also needs the muzzle regardless of how relaxed a specific park or beach is about ordinary pets. One handler may only walk one PPP dog at a time under the official decree, which matters if you're travelling with more than one dog that could be classified this way.
Carrying the municipal licence and proof of registration while out on a trail isn't just bureaucratic box-ticking — the official decree specifically requires the handler to have them available, and a park ranger or local police check in a popular hiking area is a realistic scenario worth being ready for, not a remote one.