Interesting question. I took a quick glance through some of the fight manual images I saved and didn’t see any scabbards. I don’t have any references, but I’ve heard a couple of solutions. Longsword is good from horseback due to extra length, and scabbard is attached to saddle. Smaller items, such as dagger or hammer are attached to self. If you dismount, just take the sword. Or, especially if in a tourney, put through a metal ring attached to belt (no scabbard) if you plan on using it very quickly. Again, not sure where I heard those. I tried to attach a few images of “scabbards in action” I just searched for.
I’d also be curious to know if it is addressed in any historical instruction (I’ve never tried it myself—I don’t have a proper belt fitting).
