When you are asked what date it is, do you think hardest about the month or the day? For most people it's the day, so it makes sense for it to come first.
The hour. Minutes are usually unimportant for day to day life, as long as I am in the right hour. This is not true of month-day though. I imagine most people would be caring more about day than month. The day is both more important and harder to remember, so it makes sense for it to come first.
The hour. Is this supposed to be a trick question? 90% of the time, if I give the hour to quarter-hour resolution then I've done a good enough job of saying what time it is. I don't even think about minutes.
