We buy the cheap ones from Walmart or the dollar store before we go. For the price I dont mind throwing them away after. Or sometimes we'll offer them to other people in line. If we want to go more then once, we ride a couple times in a row so that we dont have to save them for later. Or if the weather is warm, we just get wet!
I would suggest taking a little empty ziploc bag along, and when your poncho is wet, just fold it up and stuff it into the bag. That way it won't get anything else in your bag wet. Just don't forget to take it out to dry later on, otherwise the next time you go to use it, it might be a little green....
If you're on Grizzly, just run into their store and ask for a merchandise bag to hold it. They are wonderful about doing that in my experience, and I've read that others have been happily handed a bag for their wet poncho. Then you just carry the merchandise bag, or put it in your backpack or whatever.
My Mickey poncho has lasted me since September, I believe. Maybe December. Shake it off (away from people!), fold it back up (sort of a cross between a big towel and a fitted sheet in ease of folding), put it in the bag. You don't waste your money, and you don't waste plastic or landfill space!
I won't toss mine, mine is the Disney one too! LOL Even if it was a cheapy one I wouldn't toss it. I usually give those away. With mine I wipe it down after with napkins and then fold it back up, or I wear it until it's dry and look like a dork. LOL