I throw a rubber tub on my foldy cart like that. And I've gotten used to swinging the back end (heh heh) wide to make turns. I use mine to haul stuff in and out of storage and for small stuff, grocery bags, and keeping slush of everything, the rubber tub helps and seems to be fairly stable.
I also got one of these sleds for outdoor hauling at my property. I can use it on snow or grass all year:
The one I got is pretty small, the size of 1 bale of straw. They make smaller too. I no longer want a garden cart. This is a bit harder to haul around, but it does NOT run down the hill the minute I let go. even in snow it has sticking power. I've had it 5 years and other than replacing the tow-rope, it's been perfect.