The best time for statewide travel is late Oct/Nov, March and April, and late May/early June. This will avoid, for the most part, Texas's hottest and coldest temperatures and the heaviest rainfall.
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The weather changes depending on where exactly you visit, with the east generally wetter than the west due to its more humid climate. In October temperatures are cooling across Texas as the autumn period sets in, but conditions still get very warm in many parts of the state.
Are Texas beaches warm? Most people will find the ocean off Texas warm enough to enjoy swimming from April to October. That's when the water temperature is usually over 70 °F (21 °C) at any of the state's coastal beaches.
The winter climate in Texas is comfortable to many, but it does get down to freezing on some days. When it does, it rarely stays that way. The further you travel south, the warmer it can get.