What I Have Found

CHAPTER 272. FENCES AND ENCLOSURES LOCAL OPTION
272.210. Definitions
As used in sections 272.210 to 272.370 the following words and terms have the following meanings:
(1) "Lawful fence", a fence with not less than four boards per four feet of height; said boards to be spaced no farther apart than twice the width of the boards used fastened in or to substantial posts not more than twelve feet apart with one stay, or a fence of four barbed wires supported by posts not more than fifteen feet apart with one stay or twelve feet apart with no stays, or any fence which is at least equivalent to the types of fences described herein;
(2) "Stay", a vertical member attached to each board or wire comprising the horizontal members of the fence.
272.230. Trespass by stock, damages and compensation--action—lien
If any horses, cattle or other stock trespass upon the premises of another, the owner of the animal shall for the first trespass make reparation to the party injured for the true value of the damages sustained, to be recovered with costs before an associate circuit judge, or in any court of competent jurisdiction, and for any subsequent trespass the party injured may put up the animal or animals and take good care of them and immediately notify the owner, who shall pay to the taker-up the amount of the damages sustained, and such compensation as shall be reasonable for the taking up and keeping of the animals, before he shall be allowed to remove them, and if the owner and taker- up cannot agree upon the amount of the damages and compensation either party may make complaint to an associate circuit judge of the county, setting forth the fact of the disagreement, and the associate circuit judge shall be possessed of the cause, and shall issue a summons to the adverse party and proceed with the cause as in other civil cases. If the owner recovers, he shall recover his costs and any damages he may have sustained, and the associate circuit judge shall issue an order requiring the taker-up to deliver to him the animals. If the taker-up recover, the judgment shall be a lien upon the animals taken up, and, in addition to a general judgment and execution, he shall have a special execution against the animals to pay the judgment rendered and costs.

CHAPTER 270. ANIMALS RESTRAINED FROM RUNNING AT LARGE
270.210. Stallions, mules and jackasses not to run at large, when--penalty
If any stallion or any unaltered male mule or jackass, over the age of two years, be found running at large, the owner shall be fined, for the first offense three dollars, and for every subsequent offense not exceeding ten dollars, to be recovered by civil action before an associate circuit judge, in the name of any person who will prosecute for the same, one-half to his own use and the other half to the use of the county.

270.230. May be killed, when
If any such horse, mule or jackass be running at large, and cannot be taken up, he may be killed, if notice be first put up at the courthouse door and at three other public places in the county, for ten days, describing the color, marks and brands, as near as practicable, of the animal, and that he will be killed unless taken away and secured.
(http://asci.uvm.edu/equine/law/fence/mo_fnc.htm)

Missouri Cruelty to Animals Statutes
578.005. Definitions
As used in sections 578.005 to 578.023, the following terms shall mean:
1) "Adequate care", normal and prudent attention to the needs of an animal, including wholesome food, clean water, shelter and health care as necessary to maintain good health in a specific species of animal;
(2) "Adequate control", to reasonably restrain or govern an animal so that the animal does not injure itself, any person, any other animal, or property;
(3) "Animal", every living vertebrate except a human being;
Cont.
578.009. Animal neglect--penalties--costs and expenses
1. A person is guilty of animal neglect when he has custody or ownership or both of an animal and fails to provide adequate care or adequate control, which results in substantial harm to the animal.(http://asci.uvm.edu/equine/law/cruelty/mo_cruel.htm)

Farmers' Liability for Their Animals

Animals are divided into two classes -- wild and domestic. As a general rule, you have no duty to restrain wild animals still in their natural environment. However, you must restrain or confine your domestic animals in such a manner as not to create an unreasonable risk of harm to others.
When the law places a duty of reasonable care upon you, those who may be injured by your animals must also exercise reasonable care for their own safety. If they fail to exercise this degree of care, you may use this as a defense if they should sue you for their injuries.
However, if the law places an absolute duty on you to protect others from injury, the fact that the injured party failed to exercise reasonable care cannot be used by you as a defense to escape liability. Thus, the magnitude of your legal duty may have a significant effect on the outcome of a lawsuit.
Under present Missouri law, there is no longer any open range; you must now fence in your domestic animals. If they escape through your lack of care, you are liable for the damages they inflict. If the animals of another invade your property, you may drive them off your property if you do so in a reasonable manner. If they do damage, you may impound them, holding them until the owner pays for the damage.
In driving animals along or across a public highway, you must use reasonable care to avoid harm to motorists and others on the highway. You should plan such operations carefully, taking all circumstances into account. The use of warning devices will put motorists on notice of the danger and may reduce the risk of liability.
The owner of diseased animals must use reasonable care to avoid the spread of that disease. He also can incur liability by renting infected premises or by carelessly disposing of infected feed and litter. Rabid dogs, or dogs exposed to rabies, must be killed, impounded or immunized. Dead animals must be disposed of according to the rules which the law prescribes; they must not be allowed to create a nuisance.
The owner of an animal who knows of the vicious propensity or tendency of the animal to do harm is under a duty to kill it or restrain it in such a way that it cannot cause the harm threatened. Failure to do so makes the owner liable for resulting damages. It should be remembered that the term "vicious propensity" is defined quite broadly by the law.
(http://aglaw.missouri.edu/liabilityforlivestock.htm)