Horse represents partnerships and strength. He also represents power and  expanding one's abilities. Horse has innate healing powers. With Bear it is one of only two totems to have innate healing power within. 

Horse totems were made by the Zuni to trade with the Navajo who were herders and hunters compared to the more agrarian society of the Zuni. Navajo herders enjoyed having rams, horses and pigs as totems to help increase their herds. 

There are six sacred directions, each  guarded by a prey god (North - Mountain Lion; West - Bear; South -  Badger; East - Wolf; Above - Eagle; Below - Mole).  It is believed that  the hearts of the great animals of prey are infused with a spirit of  magic over the hearts of the animals they prey upon.  The prey gods are  given high rank among the gods.  Because of this, their fetishes are  greatly esteemed as mediators between people and the animals they  represent.   

Power of the Fetishes: The Zuni people feel  that the power of the Zuni  fetish lies within the heart of the Zuni Fetish, much like the power of  the animal the fetish represents.  It is believed that the hearts of the  great animals of prey are infused with a spirit or medicine of magic  influence over the hearts of the animals they prey upon.  The "breath of  life" derived from their hearts whether near or far never fails to  overcome a game animal.  The breath of the powerful prey animal  overcomes the weaker animal, piercing it's heart and causing it's limbs  to stiffen and the animal itself will lose it's strength.  The roar or  cry of the beast of prey is fatal to the game animals which hear the  cry.  It charms their senses as does the breath of their hearts.  Since  the mountain lion lives by the blood or "life fluid" and flesh of the  game animals, and by these alone, he is endowed not only with the above  powers, but also with peculiar powers in the sense of sight and smell.   Moreover, these powers as derived from his heart, are preserved in his  fetish, since his heart still lives, even though his person has been  changed to stone. (Frank Hamilton Cushing Findings)