Wiki says Sunday night so gone with Monday's reset and 2 weeks to use them up. Wiki has been known to be wrong. No game update on Monday being a bank holiday but I can not see it being in game after Tuesdays update. (I could also be wrong)
They may let you carry paper over into next years event if we have it again.
This is from the news about Presents from the Sledge:
You can earn Wrapping Paper from December 12th until 23:59 on January 15th. You can still exchange wrapping paper up until 23:59 on January 29th.
~Wolf