I think you would be better off sending them.
Firstly, I am much more likely to remember to respond if it ends up with my mail than with my xmas cards (which is where it will end up if I see you over the holidays)
Secondly, I think it is awkward to hand them out
Allycat11:Personally, I would rather receive one in the mail. DH and I do a lot of traveling for Christmas and come home with a car full of gifts, cards, luggage and other junk. I would be worried that it would get mixed in with everything and I would forget to RSVP. If it came in the mail I would put it right where it belongs and RSVP as soon as possible.
Also, handing things out is very forward. I made a HUGE mistake of passing out a mission letter when I went to Haiti (asking for prayers primarily) and a donation if they want/were able to... I fealt really awkward about it and wish I had just mailed it... I also found one hanging around afterward so I'm not sure who forgot theirs. It's just better to spend the 42 cents and stick a stamp on it.
Yeah, I think I would feel awkward passing out invites...Like people might feel like they need to open it and tell you if they plan to go right then and there, talk about pressure!
I agree with PPs, just send them out.