Yeah I've been using the cart a lot more also. I usually setup my satellite bases closer to the coast. That usually makes for an easy run with the cart since my main base is also on the coast. Got lucky enough in my most recent playthrough that all of the copper/tin I've needed was fairly close to my starter meadows base, so it's only a ~5 minute trip with the cart. Made two trips and got everything I needed (plus extra) back to base. Tried loading up the cart with ~250 copper and 120+ tin and had trouble moving up some of the smaller hills without draining all of my stamina, so I cut the load in half and that made it much easier.

Like Science Dog said, I'd definitely recommend using Eikthyr when hauling a loaded cart over longer distances.