Searching through Bowl History it seems that at one time the Cotton Bowl Classic did crown a queen but no longer does.
It appears that, at least at one time, a queen was chosen from each school that would be playing in the Cotton Bowl game to represent their school at the Cotton Bowl. (For more information, read: Queens Meet at Cotton Bowl)
Also, from 1939-1993 a "Maid of Cotton" was chosen and at least at one time participated in the pageantry of the Cotton Bowl in the parade and on the field. Maid of Cotton contestants had to compete in wardrobe that was 100% cotton (including evening gowns), and participate in individual interviews that included a one-minute speech on the cotton industry and what it means to them.
(For more information, read: Maid of Cotton Carried the Interests of a Nation)
This year's Cotton Bowl game was part of the College Football Playoff Semifinals and was played on New Year's Eve, December 31st when #2 Alabama faced #3 Michigan State University. Alabama won the game and will continue to the National Championship (roll tide!).
Past Winners of Cotton Bowl Pageant:
1951 Cotton Bowl Queen, JoAnne Hill