A horse is normally guided by the reins. The rider can also signal the horse by other means such as shifting body position and kicking with the feet (cowboys can use spurs on their boots to make such kicks even more emphatic).
To lead them from the ground you use a halter and lead rope to keep the horse near you, but they should follow you if they have been trained correctly without pressure from the halter.
The horse's harness was made out of leather.
On the horse or the person? We use saddles on the horse, but they are not harnesses. On the person, there is not any harness.
when practicing you use a nylon harness but in show a leather.
A halter
does a horse pull a cart with the harness, or does a horse push the cart with harness from the front
It means that the horse has the correct qualities needed to be a harness horse.
If you are leading (walking) a horse around, then a halter. If you are riding him, a bridle.
Just a Guide Dog Harness. Some use orange vests, but most don't. There are several things a guide can need depening on the needs of the handler.
Halter
A headcollar
The part of the tack (harness) that fits in the mouth of a horse is the bit.
A halter.