That's a tough one. Ol' Mom Nature is messin everybody's winter plans up.
Other than the ski areas most tourist type attractions are closed for the Winter. The Exibition Coal Mine and outdoor plays are closed. Might check the caverns over around Lewisburg. They might be open on week-ends.
Stables in Fayetteville and Summersville. Weather permitting they might allow a "winter" trail ride but they might be closed for season also.
Hour and a half to the north is Charleston. The Clay / Avampo Center is right off the Broad Street exit. I think it's exit 100. They have childrens museum and hands on exibits.
Building next to State Capitol (exit 99) is Cultural Center. Haven't been there for years but it used to have museum of state history.
In Beckley you have Tamarack on the hill behind Turnpike Travel Plaza. Nice, large exibit of state arts and crafts. Several shops where you can watch the artist or craftsman work. Most items are for sale.