That's right. But, the penalty is usually very light. In Oklahoma you can be prosecuted for trespassing if when an officer asks you to leave you do not leave. It's a $75 fine....minor.
In Texas they have the 30-06 law. Class C misdemeanor of not more than $200 fine. And it must be posted in both English and Spanish, conspicuously posted and in contrasting colors with block letters at least 1" high. Most of the signs I see are 3/4" high...HI HI.