I haven't got Pets (yet) but I'm also quite disappointed there's no ponies. In real life I've had four ponies, as being small I can get away with riding them still. Two Welsh (Timmie and Misty), a Dartmoor (Ellie) and a Thelwell pony of uncertain breed (Baggins). All of them were much, much harder work than horses, but also friendlier, cleverer and much more fun.
Not having breeds would make sense from a game perspective, though, as it'd probably be a fair amount of additional power to keep track of what colours a horse could be from its breed, and all the various crossbreeding and the difficulties with colour that could entail. Although I suppose they can already combine the looks of the horses to get their foal anyway, if it's like human sim genetics.