How about the Cotton Bowl itself? In the 76 year history of the Cotton Bowl there have been a total of seven Heisman winners play in the game. Doak Walker was the first to do so in 1948. He led SMU to a 21-13 win over Oregon by running, passing and kicking the ball. The most recent Heisman winner to play in the Cotton Bowl also won. Ricky Williams led the Texas Longhorns to a 38-11 win over Mississippi State in 1998.
The five guys in between Walker and Williams didn't fare as well. Only Doug Flutie (1984) won the game, giving Heisman winners a 3-4 losing record in the Cotton Bowl Classic.
Heisman Winners And The Cotton Bowl
1948: SMU RB DOAK WALKER
COTTON BOWL RESULT: Won 21-13 over Oregon. Walker ran for 66 yards and one touchdown on 14 carries, completed 6 of 10 passes for 79 yards and also kicked two extra points.
1963: NAVY QB ROGER STAUBACH
COTTON BOWL RESULT: Lost 28-6 to Texas. Staubach was 21-of-31 for 228 yards and an interception, and he ran 2 yards for a score. In all, Staubach rushed 12 times for minus-47 yards as the Middies finished with minus-14 rushing yards.
1977: TEXAS RB EARL CAMPBELL
COTTON BOWL RESULT: Lost 38-10 to Notre Dame. Campbell ran 29 times for 116 yards.
1984: BOSTON COLLEGE QB DOUG FLUTIE
COTTON BOWL RESULT: Won 45-28 over Houston. Flutie was 13-of-37 for 180 yards with three touchdowns and two interceptions.
1985: AUBURN RB BO JACKSON
COTTON BOWL RESULT: Lost 36-16 to Texas A&M. Jackson ran for 129 yards and a touchdown on 31 carries.
1987: NOTRE DAME WR TIM BROWN
COTTON BOWL RESULT: Lost 35-10 to Texas A&M. Brown had six catches for 105 yards and a touchdown.
1998: TEXAS RB RICKY WILLIAMS
COTTON BOWL RESULT: Won 38-11 over Mississippi State. Williams ran 30 times for 203 yards and two touchdowns.
I'm not sure that a 3-4 record for Heisman winners in enough to call it a trend one way or the other. Especially when you consider that Stoops is 1-2 in bowl games against Heisman winners.
The lone win came in the Orange Bowl/BCS championship, following the 2000 season, against Chris Weinke. In that game Oklahoma had a masterful game plan against the Florida State offense that kept the Seminoles Heisman winner frustrated most of the night and duped him into some key mistakes as well.
The 2005 Orange Bowl was a completely different story as Heisman winners Matt Leinart (2004) and Reggie Bush (2005) steamrolled Oklahoma in USC 55-19 victory. Of course many OU fans will tell you that game never happened as it was stricken from the record due to the pay cut Bush had to take to enter into the NFL.
In 2008 OU faced Tim Tebow, who had won the trophy the year before, in the BCS Championship game. The result was a 24-14 loss for the Sooners.
This will be Oklahoma's first non-BCS championship match-up against a Heisman winner during the Bob Stoops era. For that matter, it'll be the first time Stoops faced a Heisman winner in a bowl game outside of the state of Florida. As in the previous three match-ups, this game against Texas A&M is going to come down to schemes, personnel and game plans. There's not stat or trend that will give either team an advantage over the other, but they sure are fun to look at.