Everyone over the age of 16 needs a valid photo ID in order to be allowed on base. Don't forget your ID on the day of the wedding, or you won't be able to get to the USNA chapel!
You will not be able to drive/park on base unless the driver has a valid military ID. However, there is parking available throughout downtown and at the hotels, which are short walking distance from the Academy. Once inside the gates, the Chapel is only about a 5 minute walk.
It's usually pretty cold! Expect that there may be snow on the ground. Dress warm!