it's too easy to make fun of this thread so i'll try to give legit advice here
number one is not to wear a hot fucking fursuit when it's hot out or humid. you are literally not exposed to enough of the part of the atmosphere that will evaporate your sweat and you'll heatstroke in your fursuit. make intelligent decisions about weather anytime you go hiking, fursuit or not.
as far as the difficulty breathing, that means you need to slow down. you've literally added a factor that limits how far and how fast you can go in a given day due to the reduced airflow unless your fursuit is designed for that. a mile hike up an easy trail for the photoshoot should be more than enough for you to be able to say "I did it! I hiked in a fursuit haha!" get your cringe 4chan reactions and move on with your life.
as far as full vs heads, almost nobody here hikes in fursuits and you're not likely to get an experience-based recommendation there. my personal, unqualified opinion is that you not wear the full bodysuit for any intensive activity. this also enables better use of your hands and fingers for navigating/catching your fall/picking shit up.