I know this is a simple question but I have never been able to get a real answer for it.
The western frontier was very sparsely populated and so had correspondingly little in the way of police or other emergency assistance. If a man was travelling, stealing his horse would leave him stranded where ever he happened to be. If he was in a town, it could very well leave him without a means to return to his family or livelihood. Even if the man had money in his home town, it would be very difficult to move funds (Western Union only introduced the service in 1871, and that depended on being somewhere with a telegraph office). In a more remote location, losing your horse could be a virtual death sentence. Consider what situation you would be in if you were in a strange town or camping in the country side, you had no access to money or credit, no means of sending a message other than a letter, and some one stole your car.
The situation was even worse for frontier farmers where the horse was a necessary part of their livelihood. Deprived of their farm horse, the farmer could easily wind up in a situation where he had no money to buy another one and no means of feeding his family.
Additionally, in the period just before the Civil War, horse thievery was a favourite activity of marauders, and bandits and outlaws continued this tradition afterward. A man who was willing to steal your horse without a second thought (potentially killing you or ruining your livelihood) was a bad sort who was liable to engage in other unsavory activities as well.
In many parts of the West, citizens formed volunteer benevolent groups such as the Anti Horse Thief Association (http://www.okolha.net/ahta_index.htm). These still exist as social clubs, but originally (when they were founded in the 1850s) they existed to help catch and prosecute horse thieves as well as to assist stranded travellers. At the turn of the century (1898), the Oklahoma branch of the organization had 200 lodges and thousands of members. Law enforcement was often restricted along municipal, state, or territorial lines, and so AHTA members would work together to pass information and evidence, or transport witnesses, from areas where crimes had taken place to the location where a captured horse thief was being prosecuted.