Ryshadium are a very large type of horse on Roshar, far superior to any other horseflesh. According to  Brandon, there is Investiture involved. They are thick-hooved and choose their own riders.
Ryshadium are linked to the
Knights Radiant in some way. Only a dozen men in all of the  warcamps on the Shattered Plains were fortunate enough to ride one.
They can be trained and will obey commands, such as "Away" (making them leave the area) even during the heat of battle. They can bear the weight of a
Shardbearer easily and can communicate with them. They barely require 'handlers'.
Radiants had Ryshadium, but even kings had little access to ordinary horses.
A man couldn't really understand until he'd had one accept him as a rider. It was like wearing
Shardplate, an experience that was completely indescribable.  ”
Known Ryshadium and their Riders Edit
Name of Ryshadium
" ... white stallion ... ."
"... a massive black Ryshadium stallion, one of the largest horses that Adolin had ever seen ... ." "... two hands taller and much stronger than an ordinary horse."
"... far superior to any other horseflesh."