As long as he's not having any problems I wouldn't worry about it - just enjoy him! It could be that being part Shih Tzu is what's causing the snoring but I've had dogs of other breeds that snored too.
I've had Bostons for 20 years, currently have three of them, and absolutely adore them! People who love the smooshy-faced breeds actually find all that snoring, snorting and grunting to be endearing. I know I do! All brachycephalic (flat-faced) breeds require a little extra care and attention and if they get it, they do just fine. They are strictly indoor kind of guys and can't handle extremes in temperatures because they have problems regulating their body temperature. They can overheat very easily, have a heat stroke and die. When a dog gets hot and pants, air is drawn through their nasal passages where it is cooled down. When a brachycephalic breed dog pants, it doesn't do them much good because their nasal passages are only about a half-inch long! Of my three, Katy is the most smooshy-faced and is the only one who actually snores and snorts. She's fine as long as I don't over-tax her. She's healthy and happy and plays and romps like a puppy and she just turned nine. Something else you might look for is what they call "stenotic nares" - means their nostrils are too narrow - Katy has that too and it also can cause breathing problems. With my other two, their nostrils are little open tear-drop shaped holes. Katy's nostrils are little slits. It causes her to breathe more through her mouth which sounds like a snort. The condition can be corrected surgically but it sounds barbaric and I hesitate to have the vet do a Roto Rooter job on my dogs' nose and I don't think Katy would appreciate it either!
There are some breeds that have been "over-bred", mostly by the dog show people, where certain characteristics of the breed are over-emphasized to the extent that it is harmful to the dogs health. In Bostons, the trend for show dogs is to have an extremely flat face where their little noses are just a button and sometimes actually dented in to their face - cute but not good. English Bulldogs are the worst though. They are bred to have huge heads, massive shoulders and chests, and narrow hindquarters. This has resulted in dogs that are unable to birth their own big-headed babies and must deliver by C-section. A lot of Bostons have to be delivered by C-section too. This is why breeding theses dogs is not for amateurs or backyard breeders. With bulldogs, their body build not only causes problems having puppies, they are prone to heart problems, back issues, and joint problems in their shoulders and front legs from supporting the massive weight of their front ends. I would dearly love to have an English Bulldog one day but their lifespan is relatively short compared to other breeds and if I had one, it would just kill me to lose it at an early age.
