I just happened to see some logs on the ENSENADA cache about whether or not
Mesa parks are dog friendly.

There are some Mesa parks that have sections that are dog friendly. These
parks are few and far between and it's not the entire park, only a well
marked section of the park. 

That park (Ensenada Park) is not one of them...

See http://www.ci.mesa.az.us/parksrec/Dogs/dogs_in_parks.asp for Mesa's
rules on dogs in parks.

LazyK - Dan