You can swim with the carts btw. I pull mines all through the swamp. It also helps to keep your hands empty when pulling one, you get more torque that way.

I've had some limited luck humping one through the mountain biome too when mining silver, but it's honestly just easier to build a small stone tower with another smithy in a big mountain biome and just use your feet.

I haven't used one on the plains yet, there's no real need because you get the longship with iron nails and that has more than enough room for whatever you want.
As long as you have a coastal base set up I guess.

I've never ever built a road. just dont run over rocks and bushes and your golden. It's slooow though. but worth it when you carry 4000 weight in copper to your smelters.