I am pretty sure that you cannot get an excused absence for a wedding. But it can't hurt to try, can it?
Try to be as formal as possible. State your reason for absence, and try to write how you apologize and are sorry you missed school. When you come back the next day from the wedding, you need to make sure you complete any homework and work you missed.
If possible, plan ahead and get the homework the day before the wedding, letting your teachers know that you are going to be absent and doing the work before/right after the wedding.
would probably say you don't need to write a letter. It's going to be unexcused, a wedding is not really an excuse. Sorry.
Anyways, Good Luck!