New horse - issues in arena!
sounds to me like it is a matter of practise makes perfect!
If your horse has not previously been schooled in an arena, he will find it difficult to begin with. Out hacking, a hrose uses different muscles and generally speaking, although you will enjoy cantering through feilds and stuff, most hacking is done in walk.
Take time with him in the school...spend lots of time in walk, getting him to stretch and bend. To begin with, just 'go large' around the arena and keep circle work to a minimum, or at least until he is fully warmed up. In your canter work, again, concentrate on maintaining the canter usingthe whole school, not just on a tight circule, which he'll find difficult. Once you have done more school work, he'll begin to find it easier.
Try not to worry about him runnign away with you...if he doesn't do this in open spaces, he is unlikely to in the school. Yes, he probably will feel faster, although to some extent this can be a slight illusion...when a big open field is in front of you to canter up, it'll feel slower than fence posts and markers whizzing past in a school (hope that makes sense!!). He will probably also need to go a bit faster in the school to start with too as he'll find it difficult to take the corners...but after a few weeks, he will get better.
Try to practise some schooling whilst out hacking...i.e, trying to slow the trot down, and maybe doing some circles in an open space. Also bend and flex his neck from side to side.
You'll get there - it just takes time and practise!