In my mind, dogs don't get a lot out of Santa Claus and it would not spoil a treat for them if they were left at home. Miss M, on the other hand, is at a perfect Santa Parade age.
When my husband was a little boy he was horribly afraid of dogs. He remembers walking home from somewhere with his sister and hiding behind her because of a dog. He clearly remembers the terror. When he was old enough, his parents got a puppy and he learned to overcome his fear. But even as an adult he still feels very uncomfortable around strange large dogs.
When my daughter was a toddler, she too began to evince fear of dogs. We got a puppy and she bonded with him enough that she now does not remember the fear. I remember the hassle, oh yes, I do. I had a two and a half year old toddler, a year old baby and a puppy and not enough arms to cope with all three of them at once. I clearly recall having the two kids in a pull sleigh that winter and the dog on a leash and hitting a patch of ice as I walked. Sleigh went one way, dog the other and I did a perfect cartoon rendition of feet going faster and faster and going no where. Thud! Not to mention the time the little ones let him escape one spring evening a few years later and he became a father. But all of the trouble and mess was worthwhile to prevent my little girl developing serious dog phobia.
I know that for some people, their dogs are their companions and support. That if you live alone, a pet is a lifeline. I have a daughter who has a dog that she has named 'Friend' in Shona. She takes her dog a lot of places with her and loves her very dearly. It would probably never occur to her that her shy, sweet-faced, mostly well-behaved pet could evoke terror in a child just by running into the same park with her. But I remember her sister's terror and I have seen the evidence of a similar long-ago terror in my husband.
There was a big hassle about dogs running loose in parks reported on the radio not long ago. And a pet owner was interviewed saying that it was inhumane not to allow dogs to run sometimes. That dogs need to run and play. And I think she was right. But there are a fair number of kids out there, like Miss M and my husband, for whom the dog's freedom creates terror. And that's not humane either.
There's no easy answer to this one, for me. Do we have enough parks to split them so that some are for dogs and some for children? Even children who love dogs should not be playing on ground that dogs have shit on, however carefully the owner scooped the poop. In Barcelona, Spain, they have dog runs set aside -- children are not forbidden, but the dogs come first. In all my exploration of the place I did not find one play area for children where dogs were forbidden and as I was minding my three year old granddaughter, I was most persistently looking for children's play areas. I was in a big shopping mall in France some years ago where dogs were allowed and left deposits on the sidewalks, unchallenged. I question the priority setting, I really do.
Both children and dogs can be pestiferous little monsters and people like me, accompanied by neither, can be heartily sick of both. My rule would be to keep a leash on the whole whining, blundering lot of them, frankly. Kids need company manners. And dogs do not belong at a Santa Claus parade.