Below are other mentions of horses in the original Primitive Rule:
9. You who renounce your own wills, and you others serving the sovereign king with horses and arms, for the salvation of your souls, for a fixed term, strive everywhere with pure desire to hear matins and the entire service according to canonical law and the customs of the regular masters of the Holy City of Jerusalem. (...)
35. The Master may give to whomsoever he pleases the horse and armour and whatever he likes of another brother, and the brother to whom the given thing belongs should not become vexed or angry: for be certain that if he becomes angry he will go against God.
50. This custom among the others we command you to adhere to strictly and firmly: that no brother should explicitly ask for the horse or armour of another. (...)
51. Each knight brother may have three horses and no more without the permission of the Master, because of the great poverty which exists at the present time in the house of God and of the Temple of Solomon. To each knight brother we grant three horses and one squire, and if that squire willingly serves charity, the brother should not beat him for any sin he commits.
55. We collectively forbid any brother to hunt a bird with another bird. It is not fitting for a man of religion to succumb to pleasures, but to hear willingly the commandments of God, to be often at prayer and each day to confess tearfully to God in his prayers the sins he has committed. (...) we command especially all brothers not to go in the woods with longbow or crossbow to hunt animals or to accompany anyone who would do so, except out of love to save him from faithless pagans. Nor should you go after dogs, nor shout or chatter, nor spur on a horse out of a desire to capture a wild beast.
66. We command all secular knights who desire with a pure heart to serve Jesus Christ and the house of the Temple of Solomon for a fixed term to faithfully buy a suitable horse and arms, and everything that will be necessary for such work. Furthermore, we command both parties to put a price on the horse and to put the price in writing so that it is not forgotten; and let everything that the knight, his squire and horse need, even horseshoes, be given out of fraternal charity according to the means of the house. If, during the fixed term, it happens by chance that the horse dies in the service of the house, if the house can afford to, the Master should replace it. If, at the end of his tenure, the knight wishes to return to his own country, he should leave to the house, out of charity, half the price of the horse, and the other half he may, if he wishes, receive from the alms of the house.
In other parts of the French Rule (the total having 686 articles) such as the Hierarchical Statues (articles 77 to 197) many details are given on how many horses and pack animal each official, common Knight and Sergent Brother etc was allowed to have, including the ones on his company such as valets. The section for the Master, who was allowed four horses, alone comprises 22 articles, many on his travel and his extensive escort.
The articles on the Knight Brother (art 138-155) starts with: "Each knight brother of the convent should have three horses and one squire plus, at the discretion of the Master, an extra horse and squire." Taking care of the horses is a major responsibility. Article 146 even mentiones that if a brother is in the process of shoeing a horses' feet, he may be absent from nones (the service at 3 pm) and vespers (the service at 6 pm). Absense from other services is not permitted.
Quotes from the Rule are excerpted from Judith Upton-Ward's The Rule of the Templars, Woodbridge: The Boydell Press, 1992 as presented in its entirety in an other blog, and reprinted with permission. Illustration: The emblem of the Templars, two knights seated on a single horse, shown alongside the Beauséant; miniature from the Chronica of Matthew Paris (c. 1250–1259), source Wikipedia.