Hello and welcome!
Roses are a really broad subject because there are varieties for nearly every climate. I don't live in Texas but I've been there and know it's huge with several different gardening zones so I can't really speak to these specific varieties in that specific environment.
However, I can say that in general, most roses can do well in containers. Until last year (when I moved and gave them away) I had 6 varieties growing in 5 or 8 gallon containers. This was in Pennsylvania. The two biggest problems I had were insect predation and the pot drying out in warm weather. If I were going to do it again, I might paint the pots solid white (to deflect sunlight) and/or use bigger pots so they wouldn't dry out as fast. I would also use a lot of mulch.
This is one of my container roses from last year. It's Sheila's Perfume. I was sad to give it away, but I know the person who has it now will enjoy it.