We currently don't have a "secret santa." You know, this may sound crazy but I'm not that familiar with reddit. mk, forwardslash and insomniasexx are though. How does the secret santa work? We have lots of interactive groups etc. We have had book exchanges and hubski pen pals etc. We even write and record music together virtually in the #hubskioriginalmusicclub, but no secret santa.
Basically you signed up at redditgifts.com and linked your reddit account to it. Then when you signed up for a gift exchange (secret santa being one of many) you would get paired with someone else who signed up for the same exchange. You would then get a link to their profile where they enumerate their likes and dislikes and you would get an address to send your gift to. It will probably be the only thing I miss about Reddit. I'm seriously liking hubski from the little bit I've seen though.
We've done book exchanges and I think record exchanges. Since the community is much smaller, it was "someone picks out of a hat" style rather than a organized dedicated website. If you are interested, I would say start an informal one yourself and see if it generates interest. I would recommend waiting a couple of weeks until you see who sticks and leaves from this influx. Traditionally, some people only stick around for a couple of days. If they're here after a couple weeks, they're usually here for life.