Skate on the Eiffel Tower, Things to Do in Paris during the Holidays
I did not see dancing at the Bain Douches as one of of the activities offered in What to do in Paris during the holidays (en Anglais) by Mairie de Paris, Paris City Hall in English parlance.
First thing that caught my attention was Skate at the Hotel de Ville and then more of the winter sports with Skate on the Eiffel Tower which sounded dangerous at first until I read the fine print spelling that it's "the highest skating rink in Paris … on the first storey of the Eiffel Tower! Rink open to the public every day from 10.30 am to 10.30 pm. From 15 December 2010 to Wednesday 9 February 2011. Free entry for visitors to the Tower, but you have to buy an entry ticket to the Tower to enter the rink. Skate hire (personal skates not allowed)."
Getting back to the first Skating option Skate at the Hôtel de Ville has "a 1636 m2 skating rink awaiting you! Displays and demonstrations are in the programme: ice hockey, curling, dancing.
From Friday 17 December to Sunday 27 February 2011 – Free entry – skate hire: 5 euros. Place de l’Hôtel de Ville – Paris 4th - Metro: Hôtel de Ville (lines 1 and 11).
Times: From Monday to Friday from midday to 10 pm. Saturdays, Sundays and bank holidays from 9 am to 10 pm, do note last entries 1 hour before the rink closes."
If you are in Paris with children, merry-go-rounds will sound mighty good thanks to " Free Rides in These Locations on Wooden horses and illuminated merry-go-rounds for children of all ages on rides in many areas of the capital. From 18 December to 2 January, from 10 am to 7 pm."
(* Details on Free Rides are all in French but since it's only locations (addresses) you should be able to understand)