The Comanche are actually a tribe that only came into existence after the arrival of horses, so talking about what they did before is pointless. They completely reordered their lives around them. They were also considered the finest light cavalry in the world during the 1800's, undone only by massive technological advantages by the settlers. (Namely, repeating rifles. Before then, they were all but unbeatable.)
As for their method of war:
"The Comanche, however, were never cavalry in the European sense. They did not adopt mass tactics like the Persians, Mongols or Huns, nor did they use shock tactics like European Knights. Instead they created tactics that were very much appropriate to the wide open regions (eastern New Mexico, southern Colorado, southern Kansas, all of Oklahoma, and most of northwest Texas) to which they were native. The Comanche rode and fought very much as individuals and they never pressing a charge home-instead relying on horse archery to defeat the opposition. To the great surprise of many an opponent, Comanche tactics were often extremely well synchronised and orchestrated. So much so that even professional European soldiers had difficulty in understanding, or even describing, the Comanche’s approach to warfare.
Comanches would approach an enemy at a gallop, weaving, each warrior apparently taking no orders from the war chief. These magnificent horsemen never formed a solid line, instead they formed a swirling, breaking, dissolving and regrouping mass of separate riders, thundering across the prairie, making difficult moving targets,. The whooping riders charged, broke off before contact, dodging and weaving whilst at the same time circling the enemy, showering them with arrows from all directions. The Comanche also employed a trick of hanging over the far side of their steed by a strap or thong thus almost being protected from ball or arrow."