Can you guarantee that the file will even be open on the day that the user set?
You can use File Options to set up a script that runs each time the user opens the file. This script can perform a find to see if there is any "reminder" set in a reminder table with today's date. It can then use a time set in a time field in this table with install onTimer Script to compute the number of seconds from the time the file was opened until the reminder should appear to perform a script at that moment. The script performed by the Install OnTimer script can display your reminder message.
If you need to manage multliple reminders for the same user on the same day, this will get more complex than that.