https://www.twitch.tv/videos/1463896847 look to the end of this video:
as you can see at the end of this video
every time I start the game, or every time the character dies
the moose is refreshed as a mount animal ...!
(I had chosen the wild boar)
if I go back to the stable, and re-select the boar (for example) in the next game (or after the next death) the standard mount animal will be re-freshened ..! (the moose)