I've seen both of these being used at shows:
This one is cheap, but also very unstable and not the most "fun" to use FOLDING DURA-CART - Statelinetack.com
This one is very stable, but expensive, and the one that I saw up close in person got a bit of shavings or something caught in the tracks that the end slides into and it won't slide in all the way anymore (and believe me, she tried to get it out!), so there's always a 1" gap at the bottom that stuff can fall out of while you're rolling it around. Fold-It Barn Cart - Statelinetack.com
ETA- if you have room for a large bucket this type might work for you too: Tuff Stuff Muck Cart - Handtruck and Dollies.com
I got this one for myself (Amazon
.com:..."> Miller Manuf Co. CA500 Muck Cart: Amazon.com:...
) but despite saying that it "Folds easily for storage or travel" it doesn't fold anywhere near flat.