Well, darn -- another "I'll get there someday" restaurant is gone. On the other hand, the menu at the follow-on operation, Polliwogs looks pretty good.
The LoopNet listing for the building says that the owner of Icy's was retiring rather than business being bad at this location. It also says the building was built in 1984, which is about what I remember. I recall a promising looking restaurant starting there (not Icy's, which this site claims dates to 2004) just about the time I left town to live in Fayetteville. As for Icy's itself, it seems to me it may have started at the much-restauranted sports bar outparcel at Columbia Mall and then migrated down Two Notch, but I'm not sure of that.
UPDATE 12 June 2011 -- Here's the original Columbia Mall location for Icy's:
Also added the name Josh's to the post title based on the comments.