The term “abandoned horse” as used in this chapter means any horse, ass, mule or other animal of the genus Equus, unbranded, or, if branded, that has escaped assessment for taxation for the year next preceding the killing of such animal as hereinafter provided for, and running at large upon the open range of this state, and includes a foal running with a dam coming within the above definition. An animal not bearing a decipherable brand recorded in the office of the recorder of marks and brands shall be deemed unbranded.