Most mammals that eat have an instinctual "hoarding" ability, some more pronounced than others, some constant, and some only triggered by situations where it is necessary.

Think of the human ability to store fat - if the human body suspects it is in a situation where it is starving everyday, or even some days(not sure what the magic number is, lol) it will begin to "hoard" calories and fat so that it always has an energy source. This is essentially no different than a mouse hoarding food. There are differences though - mice hibernate in most colder climates, and in warmer ones, food can be scarce anyways, so they hoard to survive. Because of this constant starving possibility in rodents, they do it constantly. If you took say, ten generations of mice, maybe more like fifty, and ALWAYS fed them constantly, you would likely notice that instinct begin to lessen. Hard to say without actually doing the experiment though.

In any hand, yes , indeed mice DO hoard. It is a leftover survival instinct from when they were non-domesticated(if you mean pet mice) or one they still require, for the life of something as small as a mouse and that eats what it does, is quite perilous all the time.