Okay, so you've made a start on converting your equine oversized housepet into an asset to your doomstead, starting his driving training by free-driving with your riding tack. Now it's time to move onto the next step... Having the critter actually pull a load. And you can do this with minimal investment in driving gear as well.
What you will need is a breaststrap for your saddle. You may already use one for riding. I always do. Be sure to attach it to the main D-ring of your saddle (the same one as the latigo/billet of your front cinch uses), not the wimpy little D-rings at the front of some saddles, which are not strong enough for any real use.
You'll need a couple of 8' to 10' flat nylon straps or strong cords. Cheap nylon lead lines (which really should never be used for their intended purpose) will do. These will be used as traces (aka "tugs") to pull your load.
You'll need a singletree. These can be picked-up for next to nothing if you look around. (I just bought a couple of sturdy, steel singletrees at the antique junk yard for $3 apiece today.) Or you can make one pretty easily. It's just a strong pole or board as long as the horse is wide, with a ring or hook in the middle to attach to the load, and a hook or ring at each end to attach to the traces. The singletree serves to even-out the left-right motion of the horse's walk so that your load is pulled in a straight line rather than a zig-zag. It also holds the traces apart, off the horse's hind legs.
Finally, you'll need a load. A big, old tire will do. Or a wooden shipping pallet. If you're ambitious, you can slap together a simple wooden sledge out of scrap lumber (often called a stone-boat). Your load will need a loop of chain or rope at the front to attach to the singletree.
A simple stone-boat I put together a few years ago,
with a three-dollar, steel singletree.
Take your horse back out to the safe, enclosed area and warm him up with some free driving. Have the load and other stuff out there ahead of time so he can get used to it all being around.
Again, a helper will be a real boon. Attach one trace to the rear side of the main (front) D-ring on each side and run it backwards under the stirrup leathers. Have your helper stand behind the horse holding the free end of one trace in each hand. (If your horse cannot be trusted to refrain from kicking in a situation like this, you need to forget about driving for a while and back up to teaching the proper ground manners the critter should have learned as a foal... Or send the SOB to the cannery and replace him with any one of the many more deserving horses waiting for a chance to be useful.) Lead the horse around and have the helper slowly apply more resistance to the traces. Get the horse used to pulling into the traces, having them rub his sides and legs a little, especially when turning.
Now you can hook the traces to the singletree, which should already be attached to your load. After attaching, slide the load back so that there is very little slack in the traces.
It's usually easiest to start out leading the horse with a load. If you've established a proper relationship with the animal (meaning you are the dominant member of the team and he will not run over you, no matter what), you might want to stand in front of the horse's nose, step backwards, and invite the horse to step to you so that, if the feel and sound of the load spooks him, you can stop him and settle things down instantly. Most horses get used to the load dragging behind them pretty easily. Just make your turns wide and looping at first so the load stays behind and the traces don't pull into the hind legs too hard.
Once you've got the basic pulling a load thing down, combine it with driving. If you're using a stone boat, pallet, or something of the kind, you might even try "surfing" on the load a little bit.
As with all training, don't try to do too much, too fast. Make good progress and finish for the day on a positive note.
And keep in-mind that this improvised outfit is not a proper harness. Don't expect the horse to pull much or for very long with this set-up. This is just to get you started.