I've had both mice and rats as pets and although they are both rodents, of course...lol, there is a difference between how they hoard.
But, to answer your question..yes, mice do hoard.

I'm guessing though, it depends on the circumstance, such as wild mice vs. domesticated. I'm sure the wild mice hoard more due to the fact that they have far less resources to depend upon, so once they do find supplies for their need, they will hoard as much as necessary.
I've found that domesticated mice, however, can only hoard what is provided to them...such as various items for their bedding and, of course, the food which is given to them.

When I've cleaned their cages, I notice the mounds they create within and underneath their 'homes' consisting of whatever they decide necessary, I guess.

I have had issues with wild mice in my home in the past and have found that they do hoard whatever they can get a hold of for bedding and food. It's amazing how resourceful they really can be, especially if female and establishing nesting for their babies.

Hope that helps some.

Shangrala