I don't know much about the mice, but I know rats and with rats is that a young or new rat (that doesn't know you) has to learn the smell of you finger to tell apart what is food and what is your finger.
It could be also the case for older rats at times:
- when you have your fingers all dirty with some food like let's say yoghurt - then the rat (especially the greedy one) can have problems telling where the food ends and where the finger begins :)
- when you have your finger "dirty" with something that rat doesn't know (like a hand cream) but on the other hand rat knows you and know that with a finger you give him food, so it assumes that since it is not your finger (because your fingers have a different smell) so it must be a food, and then it bites.
It can also be a kind of fight / game that young animals often play with each other and so the bites aren't really bites but rather nips as you say.
I don't know where did you get your mice from but in pet shops the life for such animals can be tough so they learn some defensive reactions to hands / fingers.
And last but not least like among humans in some rare cases, some just don't like others getting too close to them so they "bite", or the "bite" just because they like to do it.