A riding horse (working or pleasure kind) should almost never need any vocalized encouragement to get goin'. If you want the horse to move forward, you shift your weight a bit forward and press your thighs against the horse's rearmost ribs. No kicking required. If a reasonable experienced horse (it's let you stay on more than 8 seconds and isn't thrashin' around anymore) doesn't respond to this, it's likely that the horseman/woman needs some additional skill development.

For "competitive" dressage, verbal commands may be used in addition to body signals, but you're asking the horse to do pretty complex stuff there, and you have to be specific. Most people use simple one-syllable "barks" rather than words.

For a draft horse, usually just a simple flick of the reins will do to go - assuming you're on the cart/wagon. Lots of farm work is done walking beside the cart, though; and you shouldn't need to have the reins in hand with a good horse or team.

Since you can't use body language to communicate with a team when you're not onboard, the "tongue click" is often used for a "go" signal, but you don't (usually) click your tongue against the roof of your mouth. You put your tongue against the roof or your mouth and you get the "cluck" when you pull (or push - people argue 'bout which way it goes) it away - and suck a bit of air in. Others may use a one-syllable "go-signal" and the most common I've heard resembles a "yup" - but it's pronounced "a-a-y-yup" or "e-e-e-yup", with a sharp ending on the "yup." "Whoa" (or woe) is probably almost universal for a stop instruction.

With a team, especially when you're working beside the wagon, there is always a dominant (lead) horse, and it's customary to call her (it's usually a her) by name. "yup Fanny" or "whoa Daisy." It's the courteous thing to do with a friend. You NEVER tell any but the lead horse what you want. That hoss will take care of the rest of 'em.

Of course it's okay to carry on any sort of conversation you like with your horse (or any other good animal). Talking about what you're doing is common since it makes the task go easier. The critters probably won't talk back, but they'll listen like good friends; and mostly they seem to understand you better than .....

John