It depends who got to pick first. If it was the Sugar, they'd take Clemson.
The Orange Bowl was pretty loose after the XII came into play. Only after about 2002 or so did they make their perma-deal with the ACC, and they also had some sort of agreement with the Big East before that fell apart. Then the XII started going to the Fiesta a lot more often too.
The Big 12 began play in 1996. All the way to the end of the Big 8, with three exceptions, the conference champ played in the Orange Bowl. And the Big 12 champ played there after the 1996 and '97 seasons.
January 1, 1968 #3
Oklahoma 26 #2 Tennessee 24
January 1, 1969 #3 Penn State 15 #6
Kansas 14
January 1, 1970 #2 Penn State 10 #6
Missouri 3
January 1, 1971 #3
Nebraska 17 #5 LSU 12
January 1, 1972 #1
Nebraska 38 #2 Alabama 6
January 1, 1973 #9
Nebraska 40 #12 Notre Dame 6
January 1, 1974 #6 Penn State 16 #13 LSU 9 (Oklahoma was the conference champion but was on probation.)
January 1, 1975 #9 Notre Dame 13 #2 Alabama 11
(Oklahoma was the conference champion but was on probation.)January 1, 1976 #3
Oklahoma 14 #5 Michigan 6
January 1, 1977 #11 Ohio State 27 #12
Colorado 10
January 2, 1978 #6 Arkansas 31 #2
Oklahoma 6
January 1, 1979 #4 Oklahoma 31 #6
Nebraska 24
January 1, 1980 #5
Oklahoma 24 #4 Florida State 7
January 1, 1981 #4
Oklahoma 18 #2 Florida State 17
January 1, 1982 #1 Clemson 22 #4
Nebraska 15
January 1, 1983 #3
Nebraska 21 #13 LSU 20
January 2, 1984 #5 Miami (Florida) 31 #1
Nebraska 30
January 1, 1985 #4 Washington 28 #2
Oklahoma 17
January 1, 1986 #3
Oklahoma 25 #1 Penn State 10
January 1, 1987 #3
Oklahoma 42 #9 Arkansas 8
January 1, 1988 #2 Miami (Florida) 20 #1
Oklahoma 14
January 2, 1989 #2 Miami (Florida) 23 #6
Nebraska 3
January 1, 1990 #4 Notre Dame 21 #1
Colorado 6
January 1, 1991 #1
Colorado 10 #5 Notre Dame 9
January 1, 1992 #1 Miami (Florida) 22 #11
Nebraska 0
January 1, 1993 #3 Florida State 27 #11
Nebraska 14
January 1, 1994BC #1 Florida State 18 #2
Nebraska 16
January 1, 1995BC #1
Nebraska 24 #3 Miami (Florida) 17
January 1, 1996 #6 Florida State 31 #8 Notre Dame 26 (Conference champion Nebraska played undefeated Florida in the Fiesta Bowl.)
December 31, 1996 #6
Nebraska 41 #10 Virginia Tech
21January 2, 1998BA #2
Nebraska 42 #3 Tennessee 17