While a student at UT, he was a member of the Alpha Phi Omega Service Fraternity and the Friar Society.

[2] He was a corporal in the United States Marine Corps Reserve from 1958 to 1959.

He was a trial attorney of the United States Department of Justice in Washington, D.C. from 1959 to 1962, and was then an Assistant United States Attorney of the Western District of Texas from 1962 to 1969.

From 1977 to 1979, he was a United States Magistrate for the Western District of Texas.

[3] On October 11, 1979, Hudspeth was nominated by President Jimmy Carter to a seat on the United States District Court for the Western District of Texas vacated by Judge Adrian Anthony Spears.