Owner here of three dogs, all large, all greyhounds. 2 are always muzzled and on the lead when in the local park, unless it is very early in the morning when we let them off for safe off lead play (still wearing muzzles). We've also done Kennel Club training classes with our third grey, who's gorgeous and adores other people, children and dogs.
We go out of our way to choose dog walking times and areas that mimimise exposure to children. Like Midori, I tend to regard them as a noisy, unpredictable nuisance. And on many, many occasions, usually as we are returning to the car, I've seen parents actively encouraging their DC to come over and stroke our dogs, even though they are on lead, walking quietly and muzzled. Sigh. What more must we do? When this happens, we always politely say to the child/ren, "No, sorry, please don't stroke our dog/s. It's not a good idea to stroke strange dogs unless you know them, and you should always ask first." Cue parents giving glare of death.
Children screaming hysterically, waving their arms and behaving like drama queens is not sensible. Any child can and should be taught how to behave around animals (not just dogs). As others have suggested, if the OP would like to, Pets as Therapy would be happy to help and introduce her son to a calm, placid well behaved dog.
Like most dog owners, I am just getting on with my day when I walk my dogs. I too hate the dogs that are out of control and bounce up off lead, and refuse to respond to their owners. There is no excuse for this, and it's dangerous, selfish and stupid.
For those who prefer dog free walking, then lobby your local authorities to introduce Dog Control Orders which can ban dogs and insisit on dogs on lead. And at the Country Park which had dogs in the playground, did you complain to the park management? Photograph the offenders? Phone a Councillor? Generally irresponsible and selfish dog owners get away with it, because most people don't bother to complain, so local authorities don't bother to use the powers they already have or the new ones they could have - this applies to dog fouling too. Responsible dog owners like myself would welcome this.