I agree completely with thrownfaraway and synchronicity in this matter. I have done Tarot readings (and palm readings) at parties and psychic fairs, and I do prefer having a private room over a public table. If you can, ask for a corner in which to do your readings during the party, and sit with your back to the corner, so that you can see how close people are and change your message with respect to the privacy of your client (even nonpaying clients are clients). I dislike having extra people in the readings, myself, because they bring their interpretations into play, and can interrupt the reading often, and if they are nosy enough, they will begin tossing in questions for their friend or family member, as well. I am fully confident in my abilities as a reader, but I've unintentionally picked up on the brash energy of the hanger-on when it overpowered the mousier energy of their friend who really needed the reading. Also, sometimes the message the client most needs to hear has to do with the person who most wants to horn in on the reading.

Just as in a situation in which you are translating sign language, you are in full view of everyone else at the function, but you never know who else out there may be able to understand sign language, so what you say to your client should be circumspect, or close to the body, if personal, I would wager. So, too, in this situation, I'd want most to get your client alone, but that may not always be possible. Keep your voice pitched so just your client can hear you, whenever possible.

Have fun with it, be mindful of confidentiality (and you never know what bit of information might be more sensitive to your client than it would be to you), and don't be surprised by the serious issues that come up. Some you'll need to slip a card to and have them call you for a more private reading later, if that's appropriate. Good luck!