The theory goes that if you remove one sense then those that remain are heightened. This has certainly been true in my experience. We are very sight dependent animals and if we really want to taste, feel or hear something more fully many of us like to close our eyes. Of course we need to feel safe while we're doing that.
I like to use the temporary removal of sight in order to sensitise students to sound. The blindfold is really just to help them keep their eyes closed. However, the trust required may take a few sessions to build up, depending on the size and social chemistry of the group, the circumstances of the workshop and other factors.
A good game for introducing blindfolds is Leader Follower. A fuller explanation can be found in my book, Adventures in Sound, (no apologies for the plug - the first in months!) but it involves pairing up, one half of the pair closing their eyes while the other leads them around a space full of obstacles and other people. The 'blind' person doesn't wear a blindfold but just shuts their eyes and the physical contact is very light so s/he can break away at any time. It's essentially a trust building exercise and has applications outside of music. Children need to experiment and it can take a while to get some of them used to notions of responsibility for someone else. With boys especially there is often a strong urge to 'get your revenge in first'.
When it comes to wearing blindfolds, some people really don't like to and it is unwise to insist. They are really just a prop, a way of making it easier to keep the eyes shut, and any exercise that uses them can be played without them. You can rely on the rest of the group to call 'cheat!' if anyone peeps.
It is very important to establish strict ground rules regarding the use of blindfolds. In particular, anyone wearing one is very vulnerable and this fact should not be taken advantage of. No physical contact, no creeping up and suddenly shouting in their ears. This sort of behaviour, annoying normally, is far worse when suddenly unsighted. In general the blindfolded person is in a passive role and it is natural to look after them. But there is a wonderful game called Bat Moth (also in the book) that I learnt from a man who is very into tracking skills. In this game the blindfolded bat is the aggressor and it is counter-intuitive not to wish them a small amount of harm if you are a moth. It shouldn't be the first blindfold game you play.
In my experience children love to wear blindfolds. It imbues a session with a sense of theatre and they enjoy the change of sensory emphasis from sight to sound.