Merkel,
This unit has a crazy history, really a three part history.
To know a battle history of your soldier you need his service records. You can order his records here at this web site, they are very fast and very fair.
The 17th Texas Cavalry split and part fought East of the Mississippi and part fought West of the Mississippi with Polignac's Brigade so by checking Pvt. Walters records you should be able to find out if he was with Polignac in the West or fighting in the Eastern battles.
I hope this helps,
Gary D. Bray