1. The rules do cover this,

Natural Tendencies
Some creatures simply aren’t made for certain types of physical activity. If it seems clear that a particular creature simply is not made for a particular physical activity, that creature takes a -8 penalty on skill checks that defy its natural tendencies.

In extreme circumstances the creature fails the check automatically.

I say canids, equines, bovines all fall in the autofail on any climb check catagory.