Not over protective...
Your friend is right. English bulldogs are fairly intolerant of any temp other than *mild* Their short muzzles, heavy flews, and labored breathing all add to a dog that cannot regulate his temp as well as other dogs. In cold weather, their muzzles just aren't long enough to warm the air before getting into the lungs, which can lead to respiratory problems. Add excitement, stress, over exertion while playing.. and you have a dog that has trouble catching his breath, and can easily overheat.
As far as other health concerns to look out for, the primary issues that most bulldogs have is nose rope/wrinkle irritation, and tail pocket problems. Just get some unscented baby wipes and some A&D diaper rash ointment. Wipe his face, under his nose rope, and in his tail pocket daily to prevent infection in these areas. Moisture, oil, dead skin and dirt build up there, and can cause a problem. If it does get a little red and itchy for him, use the diaper rash ointment to help heal and block out moisture. Not every bully has such deep facial wrinkles that they will have problems, as well as the tail pocket. Each little cute corkscrew tail is different, and it depends on how close it lays to the body. I have 2 bullies, one doesn't have a tail pocket, and one does. His tail lays so close to his body, that I can't get a finger between his tail and butt.
If allergies flare up, get him on a grain free diet to eliminate any food related skin problems... if he still has allergies a few months after getting him on a grain free diet, you can better determine it's cause. (pollen, a protien source... some dogs are allergic to chicken and chicken fat....grass.. even a wool rug or sweater)
Keep him flea free, flea bite dermatitis is common in bullies... I use Sentinel so there is nothing topical on the skin to cause irritation, and it controls heartworms, hookworms and fleas.
Hope it helps =)