Saddle bag

You can use up to 4 saddle bags on a horse to have 4 rows of storage.

The saddle bag grants 6 slots of inventory space on the horse. You can combine 4 bags for a whopping 24 extra slots.
The horse armors hover also give 6 inventory slots! So using the horse armor does not limit the maximum horse inventory, while it does increase both horse armor and rider armor.
The wooden horse armor grants +35% armor from projectiles to the rider, while the roadsign armor give +50% armor from projectiles to the rider. This stacks with the armor from projectiles the rider already has from his own armor.
This makes especially the wooden horse armor one of the best items for scrap runs early game.
What I like to do is combine a wooden horse armor with 2 saddle bags and basic horse shoes.