The problem with your usage works the other way around. If you say 'mice have got a tail' the question then becomes 'who looks after that tail for the mice? Or do they take turns wearing it?'
To use a different example, if we say 'people in that jungle tribe live in a tree house' the question becomes whether the entire tribe live in the one building. However if people in that jungle tribe live in tree houses, we know that they are not a small tribe with a single big building.
So to return to the mice, if we say that 'Mice have tails' there is no problem with this because if we have say, three mice then we have three tails - the plural for 'tail' is justified. We are not saying that a mouse - singular- has tails, but where there are many mice there will be many tails.
If you do need to clear up any ambiguity, then you need to say something like 'Mice have one tail each.'