(I am using Android 6.0.1 and Cordova 6.0.0, but I do not believe this issue is strongly version-specific.)
It is possible to change this behaviour by calling CookieManager.setAcceptFileSchemeCookies(true); early enough in the app's lifecycle that no CookieManager object has yet been instantiated. In particular, doing this at the very start of MainActivity.onCreate appears sufficient.
Is there a good reason why this shouldn't be Cordova's default behaviour? (E.g., are such cookies shared between all apps on the device?)