Your horse can't take a three step fall. You can
And Shadowmere is unkillable by weapons. Heights are his only weakness.
Not according to Wiki and UESP. Hes totally killable by weapon, you just have to be patient.
If you run off a small cliff, (enough to kill a horse, but not you), Shadowmere will die. He can also die from any other cause of damage, weapons, magic, etc. - Wiki
Unlike the http://www.uesp.net/wiki/Oblivion:Shadowmere present in http://www.uesp.net/wiki/Oblivion:Oblivion, this version of Shadowmere is not http://www.uesp.net/wiki/Skyrim:Essential_NPCs and can die. However, 15-20 days later, Shadowmere will respawn in the location of death. - UESP