To me, your sentence would imply that there are dogs that are white, and dogs that are black, but to be unambiguous about this, I would say:
There are white dogs and black dogs.
For the two colour dogs, I would say:
There are black and white dogs.
Note that black comes first when describing the colour pairing. This is still a bit ambiguous, so you could make it clearer by hyphenating.
There are black-and-white dogs.
To describe all the dogs at once, I would say either of these:
There are black dogs, white dogs, and black and white dogs.
There are black, white, and black and white dogs.
As part of a list like this, black and white loses its ambiguity.
Here's a related question.