Wisconsin burning permits and related information can be found at the Wisconsin Department of Natural Resources website.
Burn Barrels
According to the DNR we may burn only the materials that are allowed to be open burned--namely, leaves, plant clippings, paper, cardboard and clean, untreated wood. Burn barrels operate at low temperatures (400- 500 degrees F), resulting in incomplete combustion of the wastes being burned. Burning prohibited materials-- such as plastics, asphalt, rubber and other man-made materials—generates hazardous air pollutants.
Instead of burning, consider:
Recycling - newspaper, office paper, cardboard, corrugated cardboard, magazines, aluminum, metal and acceptable plastics (free at the recycle center)
Composting - leaves & plant clippings.
Chipping - brush and clean wood to make mulch or decorative chips - or use it as heating fuel in wood stoves or boilers.
More detailed information, including rules about campfires, can be found at the Wisconsin Department of Natural Resources website.