Yes
Right now, across much of the Northern Hemisphere, squirrels are doing what they do best: squirreling away seeds and nuts for the approaching winter. Squirrels infected with mange or fungal diseases, or suffering from inherited conditions, often lose their hair. Although hair loss in squirrels can look serious, the diseases that cause it aren't infectious to humans or pets. The squirrel family contains about 280 species, including ground squirrels, flying squirrels and tree squirrels, such as eastern and western gray squirrels and fox squirrels. We also have numerous squirrels with patches of missing fur. A few are quite serious with front half of body completely bare. Others have small patches missing, usually on the back. We see this with both red/brown and gray squirrels. Red Squirrels shed their coats twice a year, switching between a thinner coat in summer and a darker, thicker winter coat. 6. Males may live in an area of up to 17 hectares of woodland... that’s about the same size as 34 football pitches! 7. We have been feeding our back yard squirrels for the fall and winter and we noticed that a few of them have missing fur. One has a patch missing down his back and under both arms. Also another has some missing on his whole chest. They are all eating and seem to have a good appetite. They are all eating and seem to have a good appetite. We feed them a variety of nuts (walnuts, pecans, hazlenuts, pumpkin seeds and sunflower seeds). They also have fresh water daily. We do not feed them with feeders, we place the nuts in several places on the ground. The winter coat comes in by September and is denser and longer than the summer fur. In winter, a red stripe stretches from neck to tail and the tail fur becomes more reddish on top. Reddish brown tufts of fur develop near the ears for winter also. We have been feeding our back yard squirrels for the fall and winter and we noticed that a few of them have missing fur. One has a patch missing down his back and under both arms.
http://voices.nationalgeographic.com/2014/09/26/squirrels-animals-fall-winter-science-united-states-surprising-facts/ http://www.ehow.com/about_5090876_squirrels-lose-hair.html http://web.extension.illinois.edu/askextension/thisQuestion.cfm?ThreadID=18526 http://www.robin-hill.com/content/files/red_squirrel_fascinating_facts.pdf http://web.extension.illinois.edu/askextension/thisQuestion.cfm?ThreadID=18526&catID=213&AskSiteID=90 http://web.extension.illinois.edu/askextension/thisQuestion.cfm?ThreadID=18526 http://www3.northern.edu/natsource/MAMMALS/Redsqu1.htm http://web.extension.illinois.edu/askextension/thisQuestion.cfm?ThreadID=18526
do squirrels shed winter coats