As far as I'm concerned, it's not tomorrow until you go to bed and then get up again. I routinely log exercises done after midnight as counting for the previous day.
That´s the way my logging works too... (not that I exercise very much after midnight nowadays, but when I started logging in the beginning of 2006 I did a bit more of that).
I think that's what I have been doing, especially it it's only 1 or so. I haven't checked, but I think I may have logged some rides home as the next day if was closer to 3 or so, because then you're closer to sunrise than sunset and that makes it feel like the next day.
The next problem is if you pull an all nighter and workout on both sides. Surely they are two different days... it's not like you don't count a day if you don't sleep. (If so, I am owed lots of days.)
For ROGAINE's and adventure races, I typically split them at whatever point makes the most sense overnight (e.g., a transition in an AR, or a control point in a ROGAINE.) Other than that, I typically log any workout that begins prior to 1AM on the previous day. I don't have a hard and fast rule on it because even my late night activities rarely start later than that.
I'm impressed if you pull an all-nighter and still manage to work out both days! I think I'd sleep...