I'm thinking a template should be applied to its mount when it is converted. Should it be able to create/call a new mount?
The mount basically gains the undead type, DR/magic or silver, immunity to cold, and probably the turn resistance of the horseman.
Looking at ability score modifiers for "similar" undead templates:
Death Knight: Str +4, Wis +2, Cha +2
Dread Warrior: Str +4, Int -6 (minimum 3), Cha -4 (minimum 3).
Gravewight: Str +4, Dex +2, Wis +2, Cha +4
Huecuva: Str +2, Int -6, Wis +2, Cha +2
JuJu Zombie: Str +4, Dex +2, Int -4 (minimum 1), Cha +2
Swordwraith: No modifiers.