Nope, not that young. I was about 10. My dad co-owned another business with another man whose family was from Kentucky, and (for some reason) they were huge Razorback fans.
My Dad and I had season tickets from about '80 until the DP, and I would have sworn we attended that game with his partner's family. But it's pretty obvious that only my Dad and I went, and I don't remember it at all.
The game I attended with my Razorback friends was obviously the Cotton Bowl, given my memory of the weather.
I do clearly remember the Texas game the following year which broke their winning streak.Hated the Longhorns then, and hate them even more now.
(and yes, I'm even willing to admit he was right about the two point conversion, no matter how much I hated it)
On a side topic, since I opened the media guide to answer the original OP... we did not play in a bowl in 1981 (I assume this was probation-related). Can anyone explain to me by what convoluted logic the media guide claims a "National Championship" for the 1981 (not 1982, that one I understand) season (even the VERY same media guide says our highest rank that season was #6)?