Each applicant puts down five potential dates, ranked in order from first to last choice. (This is true at the annual lottery and at subsequent follow up lotteries throughout the year.) And no, there is no exchanging or trading of dates permitted. This is also what they call a "weighted lottery"--which essentially means your name goes into the hat more times in accordance with how many "points" you have, from 1-5--in order to give those who have not run the canyon in the past 5 years a better chance of pulling a permit than someone who ran it last year.
On the application there is a spot for a "Potential Alternate Trip Leader" (or PATL), but unless there is someone listed as a PATL on the initial application, the trip will be forfeit/canceled without the presence of the applicant. (So I can't get a hundred friends to apply for me unless they plan on running Grand Canyon.) So yes, I clustered my dates around Christmas and New Year's, with a couple drifting out into March and April, thinking (correctly, apparently) that I had a better chance of winning around the American Holiday season. But now on this side of the process I'm glad I won a Jan. as opposed to a Dec. trip: I'm only counting down 10 months and not 22!
I'm certainly tickled as this has been a multi-year journey to a permit for me.