Referee and his/her officials usually only use the perimeter of a pitch anyway as teams are often warming up on the pitch. Anyway, of course it is up to the owner to decide what is done at their ground within reason and the rulebooks.
Doubt if walking the pitch would be a big deal but as has been stated somewhere already, warming up on the pitch does cause alot of damage particularly in the goal mouth areas where teams like to spend alot of time doing set pieces etc.