I would walk him around from the ground a few laps
I take it that "outside" means hacking... start going with another, more experienced horse: a hacking buddy. Occasionally, let him stop and eat some grass. Also, go outside after your session in the ring - they're less afraid when they're tired :-)
I guess the best thing to do is getting him used to the situation he gets stressed about. Start by leading them in hand outside, with treats with you. Calm him and reward him when he's calm, he will learn that these moments are not necessarily bad for him.
You need to be patient and step by step it will get better 🙂