There is no way to identify this ornamental grass by you photos. Many grasses look similar when they are dormant. Below is a link to an article that has pictorials and information in many grasses grown in MN. Transplanting of grasses can occur either in spring or fall. In the spring wait until the plant has established regrowth (new green sprouts) prior to digging it up. https://friendsofeloisebutler.o https://mnhardy.umn.edu/varieties/grasses rg/pages/seasonal/ornamentalgrass
It looks like some type of Switch Grass.