To answer your question, since obviously you don't watch much college football at all, yes, playing Arkansas WILL hurt your image.
Let me explain.
While Kansas State plays mostly sub-par teams in an even more sub-par conference, Arkansas is playing 8-9 really good teams, mostly from the SEC. Kansas State beating Arkansas would be comparable to Mississippi State beating Alabama, not going to happen. Sorry to hurt your feelings, guys, but no one has even heard of Kansas State. Has Kansas State ever even been to a bowl game? I mean, I guess Kansas State has had some winning seasons, but with their schedule, a high school team (like Drew Central High School) could pull off a few winning seasons. Even if something crazy happened and Kansas State won the game, what would it prove? They have no REAL history of being a good, big team, and this will likely be one of the few bowl games in which they ever play. Arkansas, on the other hand, is in, by far, the most elite conference in college football. Not only that, but the same division from which both #1 LSU and #2 Alabama also hail.
Look at it like this, Kansas State and Arkansas both have 2 losses. While Kansas state lost to two pretty good teams, Arkansas' only losses were to the two teams playing in the National Championship. Kansas State is lucky that even got the bowl bid they did, while Arkansas had to accept a much less prestigious bowl than they should have, because of a rule that only allows two SEC teams to participate in BCS bowl games. What that means, since I can tell by reading some of these posts that I may need to explain myself very thoroughly and speak in very simple terms for these Kansas State fans, is that Kansas state is earned their spot, and are very happy to have been chosen for the Cotton Bowl. Arkansas, however, should be playing in a BCS bowl game, but had to settle for the Cotton Bowl.
Arkansas fans, be easy on these guys. They truly are ignorant, and have no idea what real college football is all about. They think that Kent State, Eastern Kentucky, Miami (FL), Kansas, Texas A&M, and Iowa State are REAL, WORTHY opponents. They have finally somehow earned a bowl game, and they want to be excited about it and run Arkansas down. It's the classic "trailer park trash wins the lottery and tries to act like they are not trailer trash anymore" syndrome. It will be resolved about 10 minutes into the game on January 6th when they realize that they aren't playing the buttercup teams they played during their season. The previous post by "oldy hawg" pretty much sums it all up. Kansas State has a horrible overall record, not even close to .500 (for K-state fans, .500 is a decimal number that represents your team winning at least half of their games), while Arkansas, who just through the stats alone has a much, much more prestigious program, clocks in well over .500.
As for all the negativity and Kansas State fans putting down Arkansas, I have to laugh at it, and you guys should to. Because honestly, I have been to Kansas, and if any of you guys have, then that is all I have to say. As far as the talk about the razorbacks, stupidity, and missing teeth- I would have to say that Kansas State has the same problems: Kansas State is playing the RAZORBACKS in the Cotton bowl, it is just plain STUPIDITY that they think they even have a chance, and once their smaller, slower, and underfunded football program gets on the field with a REAL TEAM, K-State's players will likely be missing a few teeth.