"Nose" is to "nasal" as "throat" is to what?
Solution 1:
Throaty and gular both mean "of the throat" with different nuances and different senses coming most immediately to mind.
Glottal, guttural, laryngeal, and tracheal are all related to parts of the throat, and hence more appropriate in some cases, while inaccurate in others.
Solution 2:
The Latin for throat is gula, and its adjective is gular. Reference
However it's more usual in humans to narrow down the area of the throat in question: epiglottal, laryngeal, tracheal, and so on. Wikipedia on the throat