It does seem like your WebMail is using a cookie with the same name as a mojoportal cookie and if it is running under the same domain it will share cookies.
Still when I look at the code in mojoportal for getting the skin base url, it looks like it should not be using the cookie unless siteSettings allows user skins:
string cookieValue = CookieHelper.GetCookieValue("UserSkin");
if (cookieValue.Length > 0)
currentSkin = cookieValue + "/";
I will look into making the cookie name more unique, like mojouserskin instead of just userskin.