I often place in my agreement form that if the costume becomes damaged, or the health and well being of the performer is threatened the performer can decide to cancel the appearance without refund. When an event host reads this they normally try to be a little more cooperative with providing some support. You also want to be able to park as close to the event as possible. Make sure your event host provides the proper parking lot passes, event passes, etc. for the performer before the person event gets to the event. Do your best to have a pickup truck or float for your mascot to ride on.
Parades can be the worst events for mascots.
Not all parades start or end in the same place. Make sure the event host provides transportation for the character back to their car. If you have a local car dealer sponsor you may want to arrange for the mascot to ride in their car. Check this out with the parade manager, in case the car dealer is not a sponsor of the parade. Also parades don't often have changing areas for mascots.