You can fish free in Wyoming when you take part in a fishing event organized by a VA hospital in Wyoming, the Wyoming Department of Health or the Wyoming Department of Family Services, or when you live at the Veterans Home of Wyoming. You must fish under the direct control of that institution.
Ask the staff of the VA hospital, state agency or the Veterans Home of Wyoming running the event to request the permit from the Wyoming Game and Fish Department. You do not apply directly as an individual.
Confirmation from the sponsoring institution that you are in its care or a resident, and that the fishing event runs under its direct control.