Hardest: Sleigh. You CANNOT make a sharp turn in a sleigh without the runners getting stuck and overturning your vehicle! This requires an experienced driver and a horse willing to listen calmly. There's no room for error if they freak out. (Obviously it's not so bad if you've got those little grocery cart wheels on it and are using it in a parade or something. I'm talking about a real sleigh, on runners, in snow.
)
Next hardest: A badly fitted, badly balanced 2-wheeler. You can put a LOT of weight on the animal's back, poke him in the shoulder, thump his spine or belly continually, transmit every bump and divot in the ground straight to the harness....yep, there's very little that's worse than a poorly designed, poorly fitted cart!
Third hardest: Probably a 4-wheel vehicle with a single horse shaft arrangement. The shafts often don't fit right on a single mini and make it hard for them to turn. The vehicle is heavier so it's harder to start, harder to stop and way harder to hold back on hills if you don't have brakes. It is also very difficult to back a 4-wheeler straight with a green horse and you can end up jackknifed. If your vehicle does not have a cut-under or fifth wheel in front it's also possible to bind it up doing tight corners and overturn. (Note: 4-wheelers aren't so bad with a pair because there's only the pole for each horse to deal with, double the horse power, and double the weight to hold the cart back.)
Easiest: A well-balanced light two wheeler with good harnessing. Obviously some carts are easier than others because of the way they're designed or fitted, but a GOOD two-wheel cart that fits properly and is correctly balanced is pretty easy to pull. There shouldn't be much weight on the back and if the shafts are where they belong the horse will be able to turn into them without getting poked or prodded. The very easiest, easiest cart to learn on is a roadster vehicle; they're incredibly light, have no basket for the horse to kick or catch their heels against and they turn on a dime. They also usually sit nice and low behind the horse which makes it easier for them to move against the shafts and very unlikely to overturn unless the driver overbalances during a runaway or runs the wheel up on a rock or something.
I would reserve a chariot, sleigh or pulled child's sled for a very experienced horse and driver combination.
Leia