I have seen some folks take a smallish rubber band, and wrap it
around the snap where they "scissor", then open the snap against the rubber
band, and clip it on the bridle. The rubber band seems to keep the snap
from coming open really easy, but you can still unsnap it if
needed.
I found, just buying really good quality snaps helps to not
have them open or break to easy. This applies to ALL snaps. When I buy lead
rope, I always open and close the snap a few times, to look it over, to
make sure it is a good quality snap. Same with snaps for reins. You will
find some really cheap snaps out there that come open way to easy, or break
under very
little pressure.