Take a look at this site- www.labs.blogs.com/its_alive_in_the_lab/2010/06/crawfish-2010.html
You can replace the crawfish with hay/cubes. The metal strainer in the metal pot is expensive but would last a lifetime.
Further down the page you see a blue plastic strainer that fits in a red muck bucket.
It is $20.50 here, www.leefisherfishing.com/products/fish-baskets Lots of commercial fishing supply places have them, and in many sizes. Fishermen use them to unload their catch.
It is $18.99 at www.seagearmarine.com/fish-basket.html
www.academysports.com has one, the H&H Lure Heavy Duty Fish Basket. Item#CHAMP40-P
Plug item# in the search box, I could not make the link work. They may have Academy Sports stores in Canada.
If not these, maybe a laundry basket with small holes?
Last idea… take a muck bucket to your local hardware store, and ask them to help you put a drain (like a rain barrel would have) on it. a PVC Ball Valve should work. You can Google an image of it, they cost about $3.00. But be careful horse doesn’t step on the valve and damage it or himself.
If you want wheels, just use a muck bucket cart, or one of those rolling trays they put under heavy flower pots.