* Horses: This was the primary mode of transportation for most people, whether for riding, pulling carts, buggies, and wagons.
* Carriages: Various types of horse-drawn carriages, from simple farm wagons to more elaborate buggies and carriages for wealthier individuals, were common.
* Oxen: In some rural areas, oxen were used to pull heavier loads.
* Walking: Especially for shorter distances.
There were a handful of experimental automobiles being developed in Europe around that time, but they were far from being mass-produced or available for use in Texas (or anywhere else) in any significant number.