You seem to have posted the very information you seek. You want to know what "battles they might have fought in" and the paragraph posted sates "Enrolled as the 9th Company of the First Mounted Volunteers, Captain Smith’s unit of eighty-three men served only a total of twenty-nine days and apparently was mustered out of service without having a participated in any battles." They didn't fight in any battles and only served 29 days in Capt Smith's Unit.
What you probably need is if this volunteer unit was changed to a federalized unit, with a change in name and command, after the U.S. Congress declared war. Or if the Windle men joined another unit after being "mustered out" of Capt. Smith's unit.
Google "Texas Volunteers in the Mexican War", lots of results, in fact there is a book with that title by a Charles Spurlin which might have yor Windle men listed.