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Sadly no. Hooves are from the Golden Age and thus and not compatible with Unchained Summoners. If you want to get something similar, your best bet is growing a pair of Arms and getting the Slam evolution, flavoring it to be a hooflike attack.
Alternatively, give it "hooves" in its physical description and take he Improved Unarmed Strike feat to use them. Bonus is that helps lead you into the Dragon Style feat, giving you an edge in difficult terrain and making your "hoof" attack get a 1.5 strength modifier to damage. Once you get Multiattack at level 9, you can actually weave this into a full attack routine.
Then again, there's something delightfully unsettling about a horse with Claws.