Lake Winnibigoshish Land Exchange Act of 2022 This bill requires the exchange of certain federal lands in the Chippewa National Forest in Minnesota. The bill directs the Department of Agriculture (USDA), if Big Winnie Land and Timber, LLC, (BWLT) offers to convey identified nonfederal land to the United States, to (1) accept the offer and convey to BWLT all right, title, and interest of the United States in and to the federal land; and (2) accept from BWLT all right, title, and interest of BWLT in and to the nonfederal land. The exchange shall be for equal value or the values shall be equalized by a cash payment, subject to an exception. The land acquired by USDA shall be added to and managed as part of Chippewa National Forest.