If you want to taste more of the white wine, serve it cool, but not icy cold. This gives you maximum perception of the wine's charms. It doesn't, however, supply the conventional refreshment of white wine. Red, of course, is another story. Too cold, and a lot of the flavor and aroma is suppressed.
Most reds are best when they are basically room temperature but the slightest bit cool.
Give these 15 minutes in the fridge. It's a jungle of stemware out there, with many manufacturers making claims for the scientifically engineered appropriateness of their glasses. Make sure the glasses are large, and make sure to fill them not more than a third of the way up. The worst that can happen is that a little cork will get into your wine. First, try to save the day by attacking the remaining cork from odd angles with your corkscrew.