You rent the whole carriage - doesn't matter if it is just you or a group of 4-5. We rode the one at Wilderness Lodge last year one night the week after Christmas - sorry I can't remember at this moment exactly which night it was. I do remember it was supposed to be the very last ride of the year, but it wasn't NYEve - we were in EPCOT that night.
It was a surprise for my 9 year old daughter who absolutely loves horses. The driver was just great! She spent the whole time talking with my daughter about how to talk her dad into buying her a horse!
I will try to read the instructions and figure out how to post a picture of the sleigh.