Snowmobiling in Congressionally designated Wilderness (CW) in Alaska is a contentious issue in the arena of appropriate use of public lands. The 1980 Alaska National Interests Lands Conservation Act allows snowmobiling in CW for traditional activities. Conversely, the 1964 Wilderness Act prohibits motor vehicles in CW to preserve its naturalness and opportunities for solitude. These conflicting mandates challenge the ability of managers to preserve CW character. The Kenai National Wildlife Refuge (KENWR) manages 534,300 ha of CW, where 253,200 ha are open to snowmobiling. Snowmobile noise degrades CW character whereas natural quiet is indicative of naturalness and offers opportunities for solitude. We determined the acoustic footprint of snowmobile noise and areas of natural quiet refugia in CW by recording the soundscape at 27 locations inside, and 37 locations outside, KENWR CW. We calculated soundscape power (normalized watts/kHz) from 59,598 sound recordings and generated spatially explicit models of snowmobile noise and natural quiet using machine-learning (TreeNet). We calculated the area of CW with the highest and lowest soundscape power for snowmobile noise and natural quiet, respectively. Snowmobile noise occurred during daylight hours while natural quiet was predominant at night. Snowmobile noise was higher in February and March while January was quieter. Snowmobile noise affected 39% of CW open to snowmobiling while natural quiet made up 36%. Natural quiet occurred in 51% of all KENWR CW of which 39% was prohibited by management or inaccessible by snowmobiles. Our models identify areas where conservation of winter soundscapes in CW can be focused.