I know I tend to go on and on about the buttery flavor of the melted cheese, so my infatuation with cold pizza runs contrary to that, but refrigeration does something magical to the crust. The cold gives the crust a little more chew, and, perhaps because you're chewing it a bit longer, the crust tastes a little sweeter. It's almost a little bagel-y. Bear in mind, I only eat my favorite kind of pizza cold- puffy chewy with a bit of internal moisture. For a crisper, drier pie, refrigeration might dry it out too much.
I think one of the best aspects of cold morning pizza is that you wake up hungry and the pizza is there. No waiting for the oven to pre-heat, no clearing of counters, no proofing of dough. There's not even any waiting for it to warm. It's just ready.