Keep in mind that 'animate' and 'inanimate' do not necessarily completely follow whether or not an item is alive or not. It is a kind of 'gender', and in linguistics, 'gender' doesn't necessarily have to do with sex, like you see in French and Spanish. In fact, David Peterson has indicated that inanimate and animate words correspond to a not-totally-explained gender system of 'grass words' and 'sky words'. Thinking on this, it is not totally implausible for hrazef to be inanimate, as a horse is a terrestrial animal and eats much grass.
There are some other horse terms that are animate, though.