"How to draw a white Dalmatian (and they don't come in other colors) with no background?"
Even documentary photos do not reflect reality at 100% (at least because in the field of human vision gets more than a camera lens), and the YAK, as a work of logical art should not just follow nature.
in addition to the contrast of the contour, it would be possible to apply a different color (say, grey shadows in the folds of wool) and partial background (for example, dog sits near the Bush). But to paint all with a solid background simply because otherwise not be solved - it is at least boring for future solvers.