@synthsin75: I don't know about mastering it within a couple of day, but thanks anyway.
Here's some theory. I've taken the formal definitions from the book
Animals in Motion.
Important concepts are "step" and "stride":
- A "step" is an act of progressive motion, in which one of the supporting members of the body is lifted from the ground, thrust in the direction of the movement, placed again on the ground, and caused to reassume, either wholly or in part, its proper functions of supporting and propelling the body.
- A "stride" is a combination of actions in progressive motion, which requires each one of supporting members of the body, in the exercise of its individual functions, to be --either alone or in association with another supporting members-- lifted from the ground in its regular sequence, thrust in the direction of the movement, placed again on the ground, and caused to resume the same relative position to the body and to the other limbs as it occupied at the commencement of the motion.
In humans, walking on two legs (i.e. bipeds), a stride consist of two steps (left foot, right foot). In four-legged animals (quadrupeds), a stride consists of four steps.
Keeping track of four legs can be a bit confusing. To help understand how a stride is performed, in each stage of the stride we can draw a diagram that shows which of the supporting members is touching the ground. The diagram also shows the direction of the movement, and numbering, to indicate the sequence of the stages (1-2-3-4-5-6-7-8-1...).
These symbols are used (left and right is observed looking at the back --anterior-- of the animal):

left hind leg

right hind leg

left fore leg

right fore leg
If all four legs are on the floor, this would be notated as follows:
The diagram doesn't tell you anything about the exact position of each part of the body in that stage, just if a member touches the ground, or not. In animation terms, it is a timing diagram. You still need to figure out the spacing and secondary actions.
Note that while humans only have four possible stages in their timing diagrams (two feet, left foot, right foot, no feet), quadrupeds have sixteen possible combinations of whether or not supporting members touch the ground.
In the above animation, I used a reference of a walk from Animals in Motion (page 28) and the next diagram (page 30).
This walk consists of eight stages. Stages 1 through 4 are left/right mirrors of stages 5 through 8. For instance, stage 5 is the left/right mirror of stage 1. This means that it is enough to have exact reference material of stages 1 through 4, because it is possible to construct the other stages by mirroring left and right.
If you check the timing diagram carefully, you'll see that each supporting member is on the ground in 5 of the 8 stages. This means the legs leave the ground only momentarily and while they do, they accelerate and decelerate. This calls for cushioning of the leg movements while they're in the air. It also means the legs move faster forwards through the air, than backwards on the ground. That seems reasonable, because propelling the body requires more force than moving a limb through the air. Air is also offers less resistance than terra firma.
It is all logical, if you start thinking about it. I guess it is this logic you're after, and you will need it to portray a walking horse in animation somewhat realistically. When you know how to do a natural walk, you can get imaginative and do all kinds of entertaining stuff to offer more bang for viewer's bucks.
Another logical conclusion is, that in order to move a limb forward, either the hips (for hind legs) or shoulders (for front legs) need to turn. This means that, while walking, the back and front of the body turn along the vertical Y-axis, in a kind of wiggling fashion, as seen from above. This means both the base of the tail and the neck move sideways during the walk. This causes all kinds of secondary actions in the tip of the tail (passive) and the head (active). The tail will swing left and right. The head will up and down and tilt a little, to counteract (and dampen) the movement caused by the swaying of the shoulders.