Texas weather is notoriously variable and extreme and so are the dive conditions.
"Dive season" in Texas runs from late Spring to late Fall, but Winter and early Spring are generally not favorable for offshore trips, though they do occur. Weather, sea state, currents, and visibility can change dramatically within a matter of hours or even minutes so offshore trips are often called on or off at the dock. Summer is usually more predictable, but depends on the presence of tropical storm systems, so always watch the marine weather forecast and keep in touch with your trip organizer for cancelations. Personally, I prefer to go out in seas of 2 feet or less for the best experience. This variability is why open water scuba checkout dives in Texas are most often done in inland lakes and springs. Some people opt to complete their open water training dives in Cozumel or other Caribbean destinations instead.
Springs like the Comal River, Spring Lake, or Balmorea offer great visibility if they are not stirred up by swimmers or tubers and will be a chilly, but constant 72 degrees year round. You may be comfortable in a 3mm full wetsuit in Summer or Fall but require a 5mm or thicker wetsuit or a drysuit in Winter or Spring. Your choice will depend on the surface temperature, wind, your cold tolerance, and how long you plan to dive.
Inland lakes, like Lake Travis, typically require a 3-5 mm full wetsuit from late Spring to Fall and a thicker wetsuit or drysuit is recommended in Winter or early Spring depending on the surface temperature, wind, your cold tolerance, and how long you plan to dive. Lakes are highly variable in temperature and visibility with temperatures in the 50's or lower below the thermocline during early Winter and Early Spring. Visibility is higher in the Winter and early Spring and poorest in late Summer and Fall as warm temperatures encourage plankton to bloom. Often you will need to stay below the thermocline for best visibility, so plan your exposure protection for the temperature below the thermocline. Click here for Lake Travis Conditions.
If you don't like Texas weather just wait a while.