Yes, it looks like it heaved during winter...they do that even here where there is NO winter. They (the Mice) like to grow on the surface. It looks like parts of the crown and roots have have shriveled up. For most hostas I'd say just yank on that and get rid of it. BUT sometimes there are tiny skinny roots beginning to grow from the shriveled crown down underneath, and if you dig up the plant they won't make it. Why don't you just toss some more soil on top of that part of the crown and see what happens in a few weeks. If nothing appears, dig up the dead stuff.

-Babka