Again I am not official.
But I went back and read the SRD
Find Steed spell. I think its somewhat more restrictive than you think.
In my Copy of the SRD they wrote:
You summon a spirit that assumes the form of an unusually intelligent, strong, and loyal steed....When the steed drops to 0 hit points, it disappears, leaving behind no physical form. You can also dismiss your steed at any time as an action, causing it to disappear.
My first post was inspired by the Paladins steed from past editions. I take this spell (in 5th edition) to mean that your riding gear and barding stays behind. I mean, its not a mount in its natural form on its home plane and the spell implies when it leaves it just vanishes. Unless someone can point me to some well reasoned errata ...?
Good news. You can put any saddle and/or barding in the chariot basket when they aren't in use. Bad news. You are dealing with "more stuff" and not less - complicating your logistics.
If your PC in question is Milandesian, Tukufu has suggested to me that I tell you to "put a squire or two" on lugging your stuff around. May I also suggest, that while its probably morally deplorable, the Coryani have few to no qualms about using a house slave or two for the same purpose? Also "nobles" generally get away with more "stuff" than humble "commoners" ... I would also suggest you invest in fancy background and buff up your Bluff and Intimidation skills.