I've always had lots of rescue dogs, cats and children about - and the golden rule is safety first and close supervision. If you can't supervise, they need their own separate areas.
We used cat nets on prams, baby gates and stable doors - and training is needed (for pets and children) so that they behave nicely together. Visiting children may not know the rules, so extra caution is needed.
The only difference with size of dog is size of jaws. Larger dogs can quickly inflict greater injuries (although, I agree, small dogs tend to be snappier).
Even with all the above precautions - there's still a small risk. Example:
My daughter, distracted by her phone, failed to notice my clumsy four year old granddaughter stray too near a sleeping fostered Golden Retriever. She stepped on his paw and fell. Hurt, he swung his head round and barked a warning.
Unfortunately, his tooth met her neck! Just a large scratch, really, not deep -but very near her jugular! We were horrified.
At the hospital, police were called (routine), the wound was cleaned (no stitches needed) and I received a police call to tell me that the dog and child should never be in the same house again.
They didn't come and take him - as he was an 11 year old, good natured Goldie - the breed made a difference. Technically, though, it was still classed as a bite, however accidental.
He was already away at the dog sitters house and I redoubled my efforts to rehome him. Luckily, I soon did find him a home in a house with other dogs - and no children.