Cooking with barleywine
Barleywines initially have a large amount of sugars in them before fermentation, and brewers balance that by adding a large amount of hops.  There is a large bitterness factor in a barleywine, which you may or may not notice, depending on your tastes and the individual brew.   If you try to reduce it like you might with a wine, the bitterness may quickly get overwhelming.   

With that in mind, I see no reason why you couldn't use a barleywine in any recipe that would work with a strongly flavored beer.

Check out The Home Brewed Chef for some great ideas for how to cook with beer.