for me it was a bit the other way around. During the last 2 travels I did with my parents (meanwhile I left the elderly place and Belgium) we took our chihuahua dog with us.
Italy was a nice experience with the dog. The Italians adored the little pet ! This really happened: a macho-looking guy drove around in his sports car, a real Italian macho guy like in bad movies, suddenly stops his car in the middle of the town's main street (blocking all traffic) to come over to us to say some cute words to our dog... Very nice travel memory !
The Danish also liked him, but the first travel with him (to Italy) was very special. Italians seem to love pets, though the local government had some less pet-friendly regulations unfortunately, some public places we couldn't go to because the dog wasn't allowed. And taking a dog with you on holiday is the same as taking a kid with you: where you're unwelcome, you don't go.