Now through January 12, 2020 - new decade, don't remind me! - there will be ice skating at L.A. Live.
Across from Staples Center, you can glide your way around a beautifully decorated tree. Skate sessions generally start at 4 or 5 PM and last 2 hours so plan accordingly and make sure to check the hours and dates before you go!
And if you don't find yourself near L.A. Live, you can also ice skate at Pershing Square or in Santa Monica. Have fun!