Don't want to write this by hand? GodCraft sets minecraft:is_saddled for you with a switch.Get GodCraftOverview
minecraft:is_saddled is an entity component: it goes in the components object of a custom mob, or in one of its component groups. Marks the entity as wearing a saddle. Check it with query.is_saddled to show the saddle on the model.
Example
Inside the components object of BP/entities/<name>.json (values are the defaults or placeholders):
BP/entities/<name>.json
{
"minecraft:is_saddled": {}
}