I'm wondering if the warm, moist air from your vent necessarily forms the ice and the only way to stop this is to heat the air from the vent because hot air must hold less moisture than warm air.
Your sequence of events can be traced out on one of these
http://www.google.com/search?client=safari&rls=en&q=psychrometric&ie=UTF-8&oe=UTF-8#q=%22psychrometric+chart%22&rls=enand this chart could tell you how many grains of moisture you need to remove from the bathroom air to stop the process.
But, this method is beyond my skill level.
Maybe you could rent a small dehumidifier for only the bathroom to test the idea or allow more house air to enter the bathroom.
Can you aim the airflow in the opposite direction and maybe modify the vent opening to prevent rainfall from entering the now upward-sloping vent?
Can you disperse the outgoing air with homemade baffles?
BTW, if you have this problem once/week or once/month or once per 'period', whatever method you choose would have to work 3 consecutive weeks/months/periods for you to be reasonably assured that it works.