I always pack a slicker, no matter what the forecast says, and normally carry it on my saddle. I always carry matches or a lighter in my pocket (not in the saddle bag) in case I get caught out overnight for some reason. Carry good canteens. I prefer the plastic with metal rims. I've had several canteens broken from the horse rubbing them on trees. Also, pack a long-sleeved shirt and a light jacket for summer and a coat for all other seasons. Better to have it and not need it, than to need it and not have it.
Always take a hoof pick with you on the saddle.
I like to leave the halter on the horse under the bridle while I ride and I keep a long (20-25 foot) stout lead rope with a strong snap on the halter with the lead coiled around the horn. I use a flat nylon halter for riding. The rope halters get uncomfortable for a horse with a bridle over top of it. The purpose of the long lead is manifold. When you take a break, remove the bridle and tie the horse to a tree, or just let the lead drag on the ground. As the horse walks around grazing, he will step on the lead, which sort of slows his movements. If he decides to walk away, you will be able to reach the end of the lead before he realizes he's caught. Many horses will not let you catch a short lead if they want to leave you, but you can catch the end of a long lead. Be sure you have at least one of the horses tied, or hold the end of the lead at all times. One horse will not normally walk away, but two together will be gone before you know it.