nope - I NEVER leave collars on mine since I did once and my best show doe got her collar stuck on a tree nub and hung herself. Never again.
If you do decide to put collars on them, use the ones with the plastic snap buckle - they can pull it open if they pull hard enough. Or put the collar round their horns.
The other thing that can happen is if they are rumbling and get a horn under the other one's collar, they can choke.
Reasons for having collars - usually its to catch them easier, particularly for goats without horns. Yours have horns - so use those as handles to catch them (but you shouldnt handle the horns before 12 mths old, as they are soft when the animal is young and can easily break). Even on my dehorned animals I dont leave collars on. Too risky.
You can also catch them by a back leg if you cant get close enough to throw your arms round the neck. Dont worry, you cant hurt them by catching them by the back leg.