It sounds like you have a great dog, and you have worked with your dog.
Good for you, that is awesome, congratulations.
It is a matter of how much liability you are willing to accept. You can take your dog out and if things look to be getting crowded or hairy, walk the dog away, and keep a bit of a buffer zone. No dog should have to be swarmed over.
There are things you can do to decrease the likelihood of your dog ever reacting, and you have already done some of them. Taking the dog to group training classes is awesome because you work your dog around other dogs and their people. You can get a feel for who among them are dog people that you might want your dog to be able to be around more, and who to avoid. Dog people are a funny breed. Most are very willing to help socialize dogs and most of them are unlikely to do anything utterly stupid, but again, you have to watch and choose.
If you have just one dog, just keep going to classes with her. Who cares if you have been through basic more than once. Just keep going. Through training, our dogs learn to rely on us to make the decisions, and we learn to trust the dog.
I, personally, would not muzzle this dog. If she was swarmed by a bunch of kids and just backed up, then the chances are very good that she is very unlikely to snap at or bite a kid that gets too close. You have to manage her so that she does not get into a situation where she feels like she must back up, but that shouldn't really be too difficult. Long before you have a group of kids on top of her, you should be able to get her out of that situation.
I think most people are a little more realistic about horses. Horses can step on, kick, bite, as well as throw you, as I am sure you know. It seems like people still bring these horses to horse shows and fairs, and they may just put a sign on the door of the stall not to pet, etc. I think people expect to watch their kids closer around horses than they do around dogs.
Dog classes and dog shows helped me gain the confidence my dogs needed me to have to take them around people. I still don't let just anyone come up to them. No reason. Same with horses, do people let everyone and anyone pet them, or ride them? No.
I have learned to turn people away with just a look apparently. Last week my 5/6 year old nieces and I took Cujo to the play ground. We were the only ones there for a while, and Cujo had never been. So he was getting used them swinging around and climbing on things, and was doing fine. When a family with a couple of toddlers showed up, we stayed on the big climbing thing, and I just kept Cujo on leash. At one point the little boy come running over, and I felt Cujo was doing enough, and shifted him behind me, and looked at the kid. Poor thing, stopped in his tracks and went back to the other climby thing.
I decided shortly after at that point that we had been there long enough and gathered my girls and headed off. Cujo is not my dog, he is my parents dog, and though I have known him since he was born, I am not willing to let other people's kids have free access to him.
Dogs really do not need to go everywhere with us. They are generally perfectly happy to stay home while we take a trip to grandma's or spend the evening playing cards with friends. They are always ready to head out with us, but that doesn't mean they should go everywhere. I find that I can relax more in some situations if I leave the critters home, and then its not all about me and my dog, then I am free to pay attention to the humans in my life.
Jenna, RN CGC & Babs, CD RA CGC HIC
Heidi, RA CGC
SG3 Odessa, SchH1, Kkl1, AD
Ninja, RN CGC & Milla, RN CGC
Joy, Star Puppy, RN CGC
Dolly CGC & Bear CGC