The map posted above details some original cattle trails that ran through Texas after the Civil War (1861-1865). This map was published by the Kansas & Pacific Railway in 1872 as part of a promotional guide to entice ranchers and drovers to utilize the Abilene Cattle Trail, which connected rail heads in Kansas (the first one was in Abilene, Kansas) to the longhorns in Texas via Indian Territory.
The Abilene Cattle Trail (aka Ellsworth Trail, or simply "Cattle Trail") is also more popularly known as the "Chisholm Trail" in American West mythology, but it never actually existed in Texas. Since cattle trailing had been an economic activity in Texas prior to 1861, the drovers established many trails to reach the railroads in Sedalia, Missouri and St. Joseph, Missouri or the steamboat ports in New Orleans, Louisiana and Natchez, Mississippi. The state is literally laced with cow paths.
Joseph McCoy, an Illinois-ian who had been a cattle dealer/handler/trader in the 1850s, recognized the need for a dedicated cattle trail route that would skirt (at least for a while) the farming and urbanizing settlements in the eastern parts of Texas and Indian Territory. Thus, he and several investors surveyed a trail from the Red River north to Abilene, Kansas. The surveyed route is represented by double red lines on this map as an almost "straight shot" through Indian Territory. Below the Red River in Texas, many trails from different starting points converged onto Red River Station in today's Montague County, Texas.
Red River Station had stores, dipping vats, some saloons, the excise man, and leather workers to supply the cattle trails. It even had a photographer, who'd take a commemorative photograph that a cowboy could pick up on his way back home.
The trails shown on this map in Texas are merely suggestions; the drovers took the trails they were familiar with and/or skirted trails due to strife or weather, so the Texas trails are very imprecise and definitely not a complete representation. None of the cattle trails in Texas were surveyed, to my understanding, and this is why there is no comprehensive map of actual cattle trails in Texas.
An interesting place is Buchanan between Waxahachie (Ellis County) and Weatherford (Parker County) where several trails converged. This town, established in the 1850s, was once the seat of Johnson County, but was dismissed in favor of Cleburne after a geographic boundary shift.
So why was this trail christened "The Chisholm Trail?" It may have been due to the drovers visiting Jesse Chisholm's store along the Canadian River in Indian Territory. Chisholm had also blazed parts of what would become the surveyed Abilene Trail during the Civil War to help several native people escape the lawlessness that had gripped the territory.
The cattle drive map is located in a few places online:
A zoom-able one at the New York Public Library
The map below stems from 1866 and is located at the Library of Congress. It shows the location of Chisholm's store along the Canadian River. Notice that it's next to several "Shawnee Towns." Before the Civil War, drovers came through this part of the territory, and this "Texas Cattle Trail" has been called the "Shawnee Trail." These unofficial names may have helped the drivers to identify and differentiate the trails.