Yes, you can hunt with centerfile rifle in Sam Houston. Please read the rules & restrictions in the booklet you get with your APH as it outlines all of that.
You did not ask, but I need to volunteer this info-in addition to your hunting license, it is also mandatory that you have an APH (annual permit for hunting). They are sold at Academy. When you buy one, they will mail you a booklet, or two, that talks about the different public hunting places and all the rules & regulations for each location.