Ok. I agree and disagree with some of the previous posters. I am a horse owner on a budget so I know what you mean! You dont want to blow your whole budget on tack when you may have other things pop up like vet bills, farrier bills etc.
I disagree with a hackamore. If he rides fine on the snaffle, stick with it. While a hackamore is great for a horse who doesnt like or need a bit...a horse that has been trained to a bit may feel a bit more in control with a hack. That is opinion and has been my experience. Its also easy to miss-fit a hack and you could really hurt your horse with the wrong placing.
Saddle wise, your saddle does sit too low on the withers. I prefer big horn saddles and you can usually find a good LEATHER one used pretty reasonably. They come in semi-QH bars which should fit your horse. Your saddle looks to have full QH...hence the saddle sliding down on his wither. You are looking for a saddle with a 6 to 6 3/4" gullet. I disagree that you cannot get a good saddle cheap. You just have to be willing to look. I just got a beautiful bighorn saddle on ebay...all leather, in perfect condition for $145. Bighorns are built for comfort. They sit deep and are made with good leather. I dislike synthetic saddles...a lot. I think the lack of maintence is the only thing I do like about them. While they are lighter...this isnt always a good thing. A leather saddle is meant to weigh down and properly distribute your weight over a large square inch portion of your horses back. When your sythetic starts curling up at the skirting (and it will!) the weight stays right where your butt sits. Stick with something that is labeled 'pleasure' or 'trail' saddle. Getting to specific on saddles "barrel", "roping" can really mess with your position in the saddle.
Get yourself a good saddle pad. I love reinsman pads and they are an abundance of them used on ebay. (can ya tell i have a problem with ebay? LOL) Even a regular new reinsman pad (not their high end models) only go for around 40+shipping.
As far as a bridle goes...if its just for a romp or two around the local trails I prefer a nylon bridle. Easy to clean, easy to change bits and if it gets too ugly, chuck it in the garbage and pick up another for $10. Leather involves cleaning and conditioning. You will be doing enough of that with a saddle!
Spend the extra few bucks and get him a proper girth. Weaver makes a smartcinch that is sooo easy to cinch up and doesnt pinch. The string girths that you have on your saddle can pinch if they arent positioned just right. They can also rot if they get wet. If the cinch breaks while you are riding, you might as well bend over and kiss your hiney goodbye!
Your horse is adorable. I just love him. Did you ever figure out what exactly he is?