You only get so many days out of the year to ice skate outside in downtown Los Angeles, so why wouldn't you? Can't you just picture yourself and your date circling around each other while David Brighton's Bowie, a David Bowie impersonator, serenades you sweetly? (December 22 only!)
Even if bad cover bands are not your idea of winter romance, and I don't know why they wouldn't be, you can always make the trip on any other winter's night.
I think I'd like to get as many friends as possible to join me for a night skate under skyscrapers. It would be just like being at home, except with more smog and taller buildings. Sure, you could go during the day, but I think you really need those night lights to make it all worth your while. Afterwards, warm up (or cool down, depending on your skating intensity) with a fine beverage at your local downtown bar or cafe.
The hours and information are here: http://www.laparks.org/pershingsquare/contents.htm