In Minnesota, a permit to carry holder may carry as many firearms they wish, of any type, open or concealed.
This means that the open carry of long guns is perfectly legal, including shotguns or rifles.
It’s important to consider that long gun carry is exceptionally rare in Minnesota outside of ranges and hunting season. The carrying of a long gun, particularly in a metro area, is likely to result in a police response involving officers that may or may not be familiar with the statutes governing this matter.