What is "jigging"?

Jigging is a bouncy pace halfway between a walk and a trot. A horse generally jigs because they are anxious or nervous or because they are over excited and want to get going with whatever the job of the day is. It can sometimes be hard to tell which, but the correction is generally the same - to release the rein slightly and use your voice to try and get the horse to relax. A horse may also jig through a downward transition - this is not correct and judges will mark it down in the show ring. A horse that has the habit of jigging a lot is a "jiggy" horse.

What is a hand gallop?

Normal, non-gaited horses have four gaits - walk, trot, canter, and gallop. A gallop is normally when the horse is going flat out as fast as possible.

A hand gallop is when the horse is galloping "in the rider's hand." That is to say, the horse is doing the four beats of the gallop and covering ground at a considerable speed, but the rider has not given the animal his head and still has control.

The hand gallop is the speed at which hunters and eventers doing cross country travel. It's thus often asked to be demonstrated in the hunter ring, showing how well the horse can cover ground while remaining under control.

What is a flying change?

When cantering, horses can canter on a specific "lead." If on the left lead, the left foreleg appears to be in front of the right. The right lead is the reverse.

A flying change is when a horse changes its canter lead without breaking stride, normally seen when changing direction. It is very difficult for a horse to perform a flying change under a rider, and it is normally only seen in well trained and fit horses. They can easily lose their balance and have to break stride or, worse, end up on both leads at once, a situation called "cross firing" or "cantering disunited" - not very comfortable for either the horse or the rider.

What is a daisy cutter?

A daisy cutter is a horse that moves in a long, low action, without lifting his hooves off the ground more than is absolutely necessary.

Daisy cutting is a very efficient way of moving, so is commonly seen in horses bred for speed (Thoroughbred, Quarter Horses, etc). It's also desirable in show hunters and in pleasure horses. It's considered undesirable in dressage, where horses are expected to show elevation.

The daisy cutter moves his leg primarily from the shoulder, not the knee as might be seen in gaited horses and dressage horses.

Is It True That Horses Always Have At Least One Hoof On The Ground?

Courtesy of tumblr user norvicensiandoran.

No.

Horses do not always have at least one hoof on the ground when moving or running (and obviously not when jumping).

At the walk, yes, a horse always has at least one hoof on the ground, but the other gaits - trot, canter, and gallop all contain what we call the "moment of suspension" - a point in the stride when all four hooves are off the ground.

The speed of a racing trot shows the moment of suspension clearly (the back hoof is a bit hard to see as its between the sulky wheels. (Image source: Wikimedia Commons).

This appaloosa is cantering and again caught in the "moment of suspension."

The existence of the moment of suspension of the trot was first documented in 1872 (when photography started to become more useful). Until then, it was only suspected.

The pace also has a moment of suspension. However, in all of the variants on the running walk, amble or foxtrot, there is no moment of suspension - which is part of why gaited horses are so comfortable over long distances.