Any person owning any horses which are running at large in any county in which the county executive has given notice of intention to make a drive, as provided in this chapter, may within 30 days after the posting or the first publication of the notice mentioned in Section 47-2-4 file with the county executive a description of such horses claimed by him, giving the marks and brands, if any, which appear thereon, and, if the county executive shall take into its possession any horses so claimed, it shall by registered letter addressed to the owner or claimant of such horses notify him that the same may be claimed within 10 days from the mailing of such notice; and such owner or claimant shall be permitted upon application to the county legislative body to take possession of such horses upon payment of the expense of caring for the same from the date of capture. If any horses are killed by order of the county executive under the provisions of this chapter, a description of which has been reported by the owner thereof to the county legislative body, and ownership of such animals can be satisfactorily established, such owner shall receive as damage therefor a sum not exceeding $10 for each animal; provided, that he has paid all taxes assessed against said animal; provided further, that payment of such claims may be made only from proceeds of sales of captured horses.