I would check the train schedule, as they do not run in the winter time for for cars or bikes. I was attempting to do the same a few months ago but the car trains were not running, I thing between October and April if memory serves me correctly.
The lowest pass in the Alps is in Austria, Brenner pass. Go through Innsbruck and straight across. No idea about weather as my plan of riding through there in December was thwarted by a storm.
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