SCA camping is basically just an event that runs over two or more days. Many people will setup medieval tents and presences to make their camp look as though it were medieval. You do not need a medieval tent to camp!. Many people use nylon tents because they are affordable and what they have. Some camping events have indoor lodging that you can book in advance. Check the Kingdom of Ealdormere event website to see what is available. Read the events website carefully to see what rules about fires etc. are in effect.
For more information about SCA camping events, read this Guide for Beginners