The instructions on ATF Form 4473 help answer this question. I suggest that you download a copy of that form.
Then, look at questions 11.b and 11.c.
11(b): "Are you under indictment or information in any court for a felony, or any other crime, for which the judge could imprison you for more than one year?" and
11(c) "Have you ever been convicted in any court of a felony, or any other crime, for which the judge could have imprisoned you for more than one year, even if you received a shorter sentence including probation?"
The punishment for a Class A misdemeanor may be found in Texas Penal Code section 12.21. The range of punishment is (1) a fine not to exceed $4,000; (2) confinement in jail for a term NOT TO EXCEED ONE YEAR; or (3) both.
Since the case you had was punishable by a term of confinement of up to one year but not more than one year, the conviction would not prevent you from owning a firearm.
If you have other questions, do not hesitate to contact me at your convenience.
Attorney at Law
5555 West Loop South, Suite 395
Bellaire, TX 77401