When it comes to how the different patterns interact, tobiano could be called the top dog. Pretty much no matter what else it gets paired with, the end result still looks pretty much like a tobiano. Sometimes the other patterns add new areas of white, like this tovero here with the bald face and white ear, but visually it is still pretty easy to identify the horse as carrying tobiano.
Here is an pony with both the appaloosa and tobiano patterns. Notice how the white areas from the tobiano just overlay the leopard pattern.
The lighting for that picture was just right to show the tobiano markings. In bright light, it would be possible to miss it. The outline is also lost as the pattern travels up his hindquarter, when it meets what would likely be the pink-skinned area on a leopard.
Here is tobiano overlapping dark-headed frosty roan.
Tobiano even stays intact when inherited by zebra hybrids. (Photo from Wikipedia Commons.)
It is tamped down and made more minimal in donkey crosses, but it is still quite obviously tobiano. (Photo by Amanda Slater.)
Which brings me back to the discussion about white Miniatures from a few days ago. I truly did not think the colt in question was a Dominant White, but rather a tobiano that was rapidly greying out. As a young foal, he looked like a chestnut tobiano. It did lead to the question, though, about what Dominant White might look like paired with tobiano. Would it overlap the pigmented areas (few though they might be in many cases), much like it did with the leopard above? Or would the instructions to make the horse white override the tobiano patterning altogether?
I suspect that the answer lies in the way the two patterns function at the molecular level. I enjoy reading papers about that aspect of genetics, but in many ways that is above my pay grade. As an artist, I am at heart someone who understands the nuances of phenotype (that is, how the horse looks) far more thoroughly than I understand the underlying mechanics. I will need to wait until someone crosses a Dominant White (particularly one of the families that tends towards the “leaky” variety rather than the all-white) with a tobiano to find out.