As long as your orig saddle is on a horse it's yours. That means that your camp horse you can remove the saddle and place it on any horse you like. That's why Wild Horses are best to tame and the White Arabian is a Wild Horse. The best saddle you can purchase at a stable is the Vaquero saddle. And get the Legends Of The East Saddle Bag. Just go to Pearson and give him what he needs to upgrade your things. Also most important go for Trinkets & Talisman. It helps your gameplay by a whole lot. Hope I didn't spoil anything ? Any Q feel free to ask.
You can go up north to the snow , and get tame & get one of best horses in the game. It's stats are elite. The White Arabian. Also when robbing someone , cover up your face so they don't recognize you.