On the off side of a sidesaddle you will most likely have 2 small metal rings. These rings are where you would attach a small leather sandwich case.
These small cases were equip with a small tin box and a crystal flask. Traditionally a lady would wrap up a ham sandwich in a linen napkin (no sandwich spread was used so the small meal would not sour!) and the flask would either contain Sherry or Tea.
Depending on the age and condition of an antique sandwich case, the cost can be several hundred dollars!
..but if you enjoy sticking to tradition, what a lovely picture it makes!