Suggest you just make a birdcage trap and bring 30-50 tranq arrows.

You can lure the snow owl with a tanky argent (2000-4000 health will do the trick) and proceed pelting it with tranq arrows once you got it in. Just be quick!

You usually won't have to bring loads of narcotics as they tame up quickly! Just keep a eye on torpor.

More Snow Owl Taming & KO Tips