I think of refreshments as being something to drink +/- something to eat. Whereas snack is something to eat +/- something to drink.
People don't tend to ask for a refreshment (they usually ask for something to drink or they name something to drink). You usually hear something like, "Light refreshments will be served in the lounge." or something like that. I think they say light to indicate to you that there won't be enough to make a meal!
Snacks can be served in the lounge too (!), but you ask for A snack, not snacks. If snacks are available that means they will be served to more than one person. What you choose for yourself would be a snack, usually. You could bring some snacks on a picnic for you and the kids - that sort of thing.