By Texas University I assume you mean the University of Texas. Their mascot is the Longhorns
My opinion would be the longhorn.. I think that is the best guess as far as I know.
Texas Tech has two mascots:
The Masked Rider
&
Raider Red
That would be... The MaskedRider. See the link below for more information:
A bull
The Texas A&M mascot is a collie named Reveille.
The mascot is the Porcupine!
The colors for South Texas College in McAllen are purple and green and the mascot is a Jaguar.
Bevo The longhorn
I think you mean Texas a&m which has ATM on their football helmets. Texas a&m's mascot is an aggie.
Texas rangers rode horses
You can read all about Reveille, the Texas A&M Mascot, here: http://en.wikipedia.org/wiki/Reveille_(Texas_A%26M)
Bevo the Bull
longhorn
The official mascot is called Super Frog and it a horned frog!
Bevo is the name of the mascot of the sports teams at the University of Texas at Austin, a Texas longhorn steer with burnt orange coloring. The shape of the Longhorn's head and horns gives rise to the school's hand symbol and saying, Hook 'em Horns. The current Bevo is fourteenth in the line of longhorns that have been the university's mascot.
A longhorn is the mascot for University of Texas (UT). Just find a drawing of the Texas Longhorns mascot and trace it, or use it to help you draw your longhorn.