How does chilling make it taste better? Does it deaden the flavor?

No, IMHO it has to do with the tannins in the wine and the different flavor profiles. Reds that are refrigerated aren't as full as those served at room temperature. Whites can be consumed at room temperature, and I actually prefer them cool but not cold.

Unless it's cheap wine.

White wine isn't a poorer quality than red. the only difference is the skin of the grapes isn't used in white wines.