Thanks for posting that link, to the 1952 train timetables page! It's a goldmine, to look at all the various timetables of various passenger rail trains you can browse from that are saved there! The Katy Lines one was interesting, and showed a lot of the trains you could take from Houston, Dallas, Shreveport, Wichita Falls, and New Orleans among a lot of other cities and towns.Oh, yes. Oh, yes! Go here for a comprehensive listing, circa 1952. But for the Reader's Digest condensed version, aside from twice-daily service over the Sunset Route (Sunset Limited and the Argonaut), there were daily (often twice daily) trains to Dallas, Corpus Christi, McAllen, and Shreveport. At that, it was a cutback from previous service; earlier issues of the Guide show service to Brownsville, Austin, and others.
As far as where you could go from Houston's Union Station, the Santa Fe would take you north to Fort Worth, Oklahoma City, Wichita, Kansas City and Chicago (Texas Chief route, also used by the Ranger) or west to Sweetwater, Lubbock, Clovis and (via through cars) onward to California. The Missouri Pacific would take you to Texarkana, Little Rock and St. Louis...largely along the route of the present-day Texas Eagle, but in those days there was a direct rail connection from Houston to Longview via Palestine. (The rails are still there, but these days they're freight-only.) The Burlington would carry you to Dallas and Fort Worth on the Sam Houston Zephyr, from whence you could make direct connections to the Texas Zephyr for Denver, while the Rock Island's Twin Star Rocket followed the same route from Houston to Fort Worth (well, almost the same route; Burlington used the T&P station in Fort Worth while Rock Island used Santa Fe's station just south of the present Amtrak station), where it diverged and continued almost due north to Kansas City, Minneapolis and St. Paul.
Lot more timetables I need to browse there, that I hadn't gotten to just yet lol.