My 3320 is covered EVERY time I blow snow. The entire hood may have 4 inches on it. Even the roof has lots of snow when I get done. I have tested the alt. when the tractor is running and I get 14.7 to 14.85 volts depending on how much stuff is on. I have not yet gotten a reading when it fails, but will try to get one.My 3520 Cab has been used to blow with the front 59" blower two seasons now. There has been times the whole front of the tractor is covered in blown snow. So far no problems like above. A cooling fan coming on would place a high current draw intermittently. The problem seems from the description to be in the alternator. Can you test voltage when the machine is running normally coming out of the alternator (should be around 14v) and then when the problem is occurring?
My cooling fan is belt driven, so that would not impact current draw. I am still leaning towards the alternator or ecu. I still have lots of winter to play. Hope I can figure it out!