Hehe - I had the same issue on my previous PDAs, and I have a BIG contacts list/family. Irritiating alarms at midnight ... I know how you're suffering.
I never found a way in WM, but it's probably a setting somewhere... default reminders on/off/period perhaps.
Eventually I just edited all the Contacts in Outlook and switched the Reminder off for all birthday events. Do it on the PC in Outlook as it's much easier & faster than tapping on the PDA. Since then my birthday reminders don't go off at midnight.