Being the subject of a statue
is enough for most mere mortals, but for military/political heroes it is often found inadequate - it is for these larger-than-life leaders-of-men that the realm of equestrian statuary
became dedicated, showing their subjects not standing on their own two feet like any old schmuck but riding on the back of a mighty equine
steed. Washington, D.C. has been described as being "supersaturated" with equestrian statuary.
There are codes and conventions in the symbolic code of this sculpture genre's use of posture, clothing and body language which will often (but not always) indicate some biographical information as to the subject's life and ultimate fate.
Look at the horse's hooves. Are they all on the ground (plaque / pedestal)? If this is the case, it doesn't only indicate that the sculptor didn't have materials and techniques available permitting the balancing of the colossal and massive metal or stone weight of the statue on fewer than four solid points - it almost canonically tells you that the sculpted individual may have ridden a horse, but died in circumstances far removed from the horseback-riding field of combat - a peaceful death, instead, often of old age. These lucky souls should, according to the conventions, be portrayed without arms wielded and with their head covered.
A horse with three legs on the ground will, of course, have one leg raised - in statuary, always a foreleg. (If your horse only has three legs, you probably shouldn't be riding it - returning it to the factory maybe, but you'll need to hitchhike there.) The rider of such a steed will have, at some point in their life, suffered a serious wound in combat. I may be mistaken, but I believe this position also applies when the war wound lingers and results in death (from infection, gangrene, application of pre-modern medicine, etc.) As above, the rider will again be presented with head covered but this time with weapons out and brandished menacingly. The position is derived from the medieval chevalier technique of the courbette, where the knight's horse discourages foot soldiers from approaching by lashing out with a foreleg.
As an interesting aside, this is the position of an equestrian sculpture (by A. Augustincic, an ironically appropriate gift from onetime Yugoslavia) representing an avatar of Peace located at the site of the UN buildings in New York - the artist suggesting that "Peace is always wounded, but never dead."
A horse is much more impressive when it's towering up on two legs (its hind legs - it's a horse rearing up, not a donkey kicking back) and the symbolic meaning of such a position is comparably weightier - indicating the death of the rider in combat. In this circumstance only is the rider's head permitted to be depicted uncovered, and they must be shown not merely riding, but engaged in some sort of action (Yow, where'd that batallion of Turkish archers come from? Woah, turn around horsie! Gid-yap! Gid--urk!) - I am unaware of rules governing their presented weapon use. This position also has knightly ancestry in the levade, where a cavalier's mount rose to 45-degree angle, raising the rider above their enemies and permitting them to survey the battlefield.
If you see any equestrian sculptures involving horses on one or no legs, the sculptor is pulling something silly on you and violating a few physical laws along the way.
These are all the rules for equestrian sculpture I could turf up online but I think there are a couple of other regulations for certain circumstances - I recall, for instance, an almost-unique but not-unknown pose employed in the representation of figures who died by being crushed beneath their own fallen mounts. As well, I am curious as to what happens when a four-feet-down sculpture is made of someone who has not yet died or been wounded in combat but later is - are hammers and welding torches applied to retroactively alter the horse's position or is the statue re-sculpted and re-cast? Please /msg me if you have any insight into these monumental concerns.
Ichiro2k3 says: The whole thing about how many feet are up is, to be cute, horse shit.