I think you're right in that we should include draft horses and separate them from riding horses. With the whole breeding thing I'd say it'd be okay to have them technically count as different species, because presumably the dwarves that bred them into two different breeds will want to keep them two separate breeds and won't let them breed together. It's a bit sketchy, but hey. (Geddit? 'Hay'?
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Then again I'm inclined to agree with Footkerchief, since at the moment we don't really need to distinguish draft horses from riding horses anyway. All they do at the moment is mull around and serve as meat and pets - they neither serve to ride upon nor to draw ploughs or what have you, so with the current technology available to dwarves there'd be no point in embarking with any specific horse, or even breeding a specific horse to do a specific job, because there aren't any jobs for them.
Come to think of it, since DF is mainly set in a medieval setting, wouldn't they -only- use draft horses - and probably not even have bred riding horses? Since at the time they would have used basically draft horses (except possibly stronger and bigger) for riding, since a modern riding horse wouldn't be any use in battle, with a knight on top. I realise our history is somewhat irrelevant to dwarves', but I don't see the point in dwarves breeding riding ponies when they've got better things to do. Like drinking, or starving to death, or engineering goblin death chambers.
Although as you can see I do think draft horses are important, I'm not so much a fan of your ideas on breeds for other animals, Raminagrobis. Wouldn't dwarves only embark with / breed dogs that are useful, as in big tough dogs or small fast ones, like greyhounds - both for hunting or killing? I think you could encompass all breeds of dogs dwarves use or see as one general 'dog', because although dwarves adopt them as pets, they were bred as killing machines (or to be eaten, if you're that way inclined), not as poodles or what have you.
And a lot of the breeds we see today are products of our societies and cultures, and because we've had rather a large time to breed them in. The hairless pig you'll see in an abattoir today is (or, uh, 'was', rather, if it's in an abattoir) a descendant of the olde worlde wild boar, but dwarves won't have had time to breed things like that in peace. I don't think we can use all, or even many, of the real-world breeds of animals in Dwarf Fortress because they're sort of irrelevant.