what I hear from most players is that you should AVOID spending your own loompoints. A +1 item will barely cause an increase in performance. Your best bet is to hold onto the loompoint and save it for when you find a cheap trade on the market for an item you really want.
If you are going to stick with CRPG and can be patient, it is a LOT more efficient to wait 2 generations and trade 2 loom points + gold for a +3 item. The only time it would be better to use 3 points yourself is if the item you want is really rare. I had to use 3 points to make a +3 steel buckler, because I couldn't find anyone with one to trade for months. Bows and arrows are easy to trade for. Horses aren't too hard to find. Desert horse, steppe horse and arabian horse are all available on the marketplace.
As for what to get first, I would recommend a horse if you plan to stick with horse archery. It will greatly increase your speed and maneuverability. Your horse also gets extra durability which is a big deal. If your horse dies as a HA, you are basically a foot archer with bad stats.
Bow and arrow are both worth the investment. I'm not sure which I would get first after the patch, but I guess I'd get arrows. The extra ammo helps a lot with horse archery.
If you can join a large clan, almost all of them have +3 horn bows and some kind of arrow available in the armory. You can test out +3 bow and arrow without spending a lot of time buying them yourself.