Most likely the weather will be cold, but roads will be clear. If it does snow, then just stay in where you are for a day, and the road departments will clear the roads.
West of Ft. Riley is Abilene, Eisenhower Museum, Old Town and such. Ft Riley itself has museums. East of Ft. Riley is Manhattan and Kansas State University. Most things to do in that area will be museums or historical sites and events unless K-State happens to be putting on a musical or some such event.
I grew up in that area, it is rich in culture, but a long way from Broadway.
Thanks! My wife and I are FAR from cultural snobs. Last summer we spent two weeks driving around rural Nevada, and loved it! Did the Vegas thing and that was nice, but we had more fun checking out the numerous ghost towns. We're history buffs, so museums fit the bill...