It looks as if your harness is a bit small and your cart is a bit big for your pony, but hay we all use what we have till we get what we want right?
All posters gave great advice, but I am going to try and get you harnessed one step at a time in the order, I would adjust this harness.
First thing your horse is to far back in the shafts. Move him forward till the point of the shaft is at the point of the horses shoulder. DSC01795.jpg
This will now make your traces too short. To extend the traces, I would go to the hardware store and get a length of chain. get the chain that each link is an individual link and welded to close it upon itself, DO NOT get the chain where each link is linked to the next, so that if you cut one link it cuts the next link too, Do not get chain that is rated less that 500 pounds, this will most likely eliminate the chain you are not to get. High-Tensile Chain - Bing Images
Cut chain to the length needed to make your traces long enough.
Looks like maybe 6-7 inches. Now you need to connect the chain to the end of your traces, you can use a few things, I like something called a Quick link
best. quick link - Bing Images
Make sure the link is closed at all times when driving.
Here are a few more connectors you can use. pilgrim 005.jpg pilgrim 008.jpg
After you have connected the chain to your traces take the appropriate link at the end of the traces and attach it to the cart singletree. This is very important, with using metal on metal at the single tree, tape the two together using electrical tape.
This makes sure the link of the chain will not slip off the single tree. I actually do this on all my vehicles, every time I drive. I once was driving the Clyde with chains on the end of his traces and looked down to see we were dragging a trace, made my heart skip a beat. What saved us was the pieces of leather that go around the singletree and the cross bar of the cart, keeping the two together. It is hard to tell what kind of singletree ends you have on your cart. This quick fix will work if you have hook ends. IT WILL NOT WORK IF YOU HAVE SWORD ENDS ON YOUR SINGLETREE, too much chance of the chain slipping off the singletree.
It looks like yours has hooks.
Just a few wraps of tape will work, you do not want to wrap it so many times you cannot get it off in an emergency. I wrap about 3 times and fold the loose end of the tape in half so it is easy to find and grip. DSC00981.jpg
Here is a photo of the leather straps that keep the singletree and the crossbar together. DSC01694.jpg