If you get a good one then yes they are safe, I like the Gatsby ones, they are nylon but have a Leather headpiece making them field safe, they are only £3 so nice and cheap to!
I have one although I haven't really used it. Has velcro replacing a cheek piece so if it does get caught it will come undone. There's two strengths as well. I have one of the Fieldsafe ones (I think that's the one).
I use the Libbys field safe head collar, it has velcro instead of clip or buckle.
The only problem I find is I have to rubber band over the velcro or she rubs it off when she rolls, the bands will break if she gets caught up.
I only use this in summer though so I can use a sunshield for her pink muzzle
I have a Horseware Field Safe Headcollar for my horse.
She wore it through the summer as she has a fly mask attatched to it or at least a flap to cover her little pink muzzle.
It seemed perfectly fine, but there again she doesnt seem to scrabble around enough to get caught up on anything.
I have a fieldsafe one with the rubber bands. Great headcollar but it did rub the pony's nose so I had to sew some fabric round the nosepiece. I think it would break really easily - although the pony never actually tried that!