The simple answer is to have more effective cavalry in warfare. I can't comment on the resulting population of miniature horses, but I do want to unpack what's going on with this legislation.

The act you mention, (32 Hen. VIII, c. 13, printed in Statutes of the Realm, Vol. 3, pp. 758-760) was actually the second act of Henry VIII's reign to regulate horse size. The first act (27 Hen. VIII, c. 6 - passed in 1536, Statutes of the Realm, 3:535-536) was similar in its requirements about horse breeding. The act of 1536 required that anyone (including clergy) who owned an enclosure kept for deer (which was at least one square mile) must have two mares that were able to breed, and that were at least thirteen hands high. Anyone with a deer park of four square miles or greater needed four mares of the same qualifications. Should any of the mares die, they had to be replaced within three months. The owners of the mares were expected to prevent any horse under fourteen hands from mating with the mares. Failure to prevent this (or to keep the requisite number of mares) would result in fines.

The 1540 act differed slightly from it's predecessor. The statute begins by forbidding any person residing in the specified lands and counties (too numerous to mention here, but it covered a fair portion of England) from allowing a stallion over two years of age but under fifteen hands high from grazing in the commons, marshes, waste land, etc. The goal was to prevent any person who owned a horse of poor stature (in the eyes of King and parliament) from breeding with any mare (of thirteen hands high). Anyone who should find a horse in violation of this act could go to the local king's official (eg. forest warden, local balif, etc) and have them measure the horse. If the horse was found to be in violation of the act, the person who discovered the horse could keep the horse as their property. There is an exception for well meaning owners to report their horse had escaped and thus claim their horse back, but they had a limited time to do so. There is a further proviso that allows for the killing of mares and foals that would be unfit for breeding. The act closes by stating that horses not meeting the above requirements can be kept as work horses, so long as they are not kept in the same pens as the desirable mares.

The preambles to both statutes explain that their prohibitions were intended to correct the "decay" of horses that had occurred in England over the years (whether true or not). Henry and the members of parliament believed that the horses of England were shorter than they needed to be in order to be useful, and they were aware that people were keeping smaller horses because they could still work at the plow or as transport. Henry and the members of parliament were less interested in the agricultural value of the horses, and far more interested in their value as war machines. Horses had to be of sufficient size, in the military thinking of the time, in order to be useful in war. Henry went so far as to spend 200 pounds on Spanish war horses in 1540 (L&P 16:187, 195).

The main reason for these acts was because the defense of the realm depended on (among other things) proper war horses. Henry possessed no standing army. It was the nobles and landowners who were expected to muster troops and horses should the need arise. That is why the laws were designed to facilitate proper horse breeding, and even contained provisos for the legal theft of misplaced property (though the law was likely designed to prevent people from letting their horses graze upon common and waste land, rather than to facilitate horse theft). Even after Henry's war filled reign, royal officials tried to ensure that elites maintained the proper quota of war horses (Gunn, The English People at War, pp. 60-61). Whether the act was successful is harder to judge. This was a difficult law to enforce, as there were thousands of people who owned enough property to be subject to the 1540 statute's requirements. The later attempts to enforce in 1547 and 1565 indicate that royal officials attempted to enforce the statute, but it's success at creating "better horses" is much harder to judge.