How often do birds of prey snatch small dogs?

It's not very common, as long as their owner is competent.

If a person lives in an area with large raptors like Eagles, Osprey, Great Horned Owls then I would be concerned, it does happen, not sure of the stats but I would be careful.

Not often enough.

Every Time they have a chance or opportunity. Coyotes also snatch up small animals.

Unsure. That being said, me Basset Hound puppy was snatched by an eagle who flew him to her nest. I had to climb the mountain and retrieve him from her nest. When I arrived me Basset Hound puppy was eating her eagle eggs. 

I doubt there are any stats. about this but it might happen, so if you have a small dog or puppy, and this kind of bird around, don't leave it out there alone.

Not very often. There are a lot of eagles where I live. In 13 years, I have only ever heard of one such incident.

heard about critter a dog I think taken by a bird of prey

Depends on where you live and if you leave your dog unattended outside with hawks or whatever circling your yard.

i wouldnt think it happens that often