Outlaw Man

Set in America during the pioneering era, "Outlaw Man" is pursued by the Pinkertons after he is awarded with a prize. Despite the man escaping without leaving any footprints, the detective agency manages to find a small trace of his escape and persistently chases after him. The man's beloved horse, Cameron, is eventually shot and killed by the detectives, leaving him in a desperate crisis.

(Addendum from mangapedia):

This is Hirohiko Araki's second debut short work, published in 1982 when he was still under the name "Toshiyuki Araki". It is a wild west manga following his first work "Poker Under Arms". The original genko (manuscript) of this work was lost, and for a long time it existed as a "phantom work" that had not been collected into tankobon. 2004 saw the digital reprinting of this work from the magazine in which it appeared in and is part of "Gorgeous Irene".