Here are the bones to my filly rig.  It probably looks like it has way the heck too many joints in the legs, specifically the forelegs.  Nope.  And yes, even the squashed proportions of the filly have enough room to fit all those joints.  The show is actually remarkably accurate with its animations, clearly basing them on actual horse movement and joint placement (with obvious leeway for the more exaggerated cartoony poses.)

My simplified bone structure for the foreleg goes:

Shoulder (scapula)

Upper arm (humerus)

Lower arm (radioulna)

“Hand” (metacarpus)

Hoof

And for the rear leg:

Pelvis

Upper leg (femur)

Lower leg (tibia)

“Foot” (metatarsus)

Hoof

Note the joint placement.  The “wrist” joint is smack dab in the middle of the foreleg.  Many 3D pony rigs tend to place it far too low.  Likewise, the ankle is midway down the rear leg, though that’s one that almost everyone gets right, due to the prominent heel bone.