Full-time student status in another state with income in both home and school states, do I have to file a WI income tax form?

No, but he might. Unless there is a reciprocal agreement (and Wisconsin and MInnesota do not have one with one-another) income is usually taxed in the state where it's earned, as well as taxed in the state in which you live. You do not need to file a WI return, but your son may need to in order to claim the income he earned there.