Some things are only stored on your horse in Red Dead Redemption 2. These items include Horse Revive Tonics, Health Tonics, and Stamina Tonics. Your horse brush and horse food is also stored on your horse. They can only be used when near your horse and can be accessed when riding or near your horse by opening the weapon/item wheel by pressing the LB/L1 button and then using the RB/R1 button to tab over to the horse menu.
Other items that your character can use are stored there as well. These include masks that you can wear, multiple outfits, and various hats that you collect. To store new clothing items on your horse, you’ll do it automatically. When you get a new hat or mask, you will store and access these items from your horse. To store new alternative outfits on your horse for cold or hot weather environments you can do by purchasing them from the Tailor or Trapper.
When at these vendors you can select which new outfit you want to purchase/craft, and can equip that item on your character on the spot. If you’ve purchased items like a hat, for example, it will automatically be added to your horse inventory. However, if you want to arrange your storage you will need to go to your wardrobe. This can be at your campsite, home, or hotel.
When using the Wardrobe at one of these locations, you can remove outfits from your horse, equip, and add outfits to your horse’s inventory.