With render controllers, you can hide certain bones in the "part_visibility" array. It's syntax is very similar to the "materials" array.
Let's analyze "part_visibility" in this fox's render_controller:
All bones that start with "leg" will visible when !query.is_sleeping returns true (the ! reverts the value: when query.is_sleeping is true, !query.is_sleeping is false) , or, in other words, the fox isn't sleeping. When the fox IS sleeping, the !query will return false and legs won't be visible.
If the fox IS sleeping, the query will turn to true and the bone named "head_sleeping" will become visible. Otherwise it will be invisible.
If you wanted the "arctic" variant to be headless, you could include this in "part_visibility":
{ "head": "!query.variant == 1"}
which would do practically the same as:
{ "head": "query.variant == 0"}