I ski regularly in Austria.
If I was on a package (rare these days) I would go to Innsbruck.
When I travel flight only I go to Munich or Salzburg.
Salzburg has less weather risk than Innsbruck and Munich is an easy drive into the Tirol - rental cars are considerably cheaper in Germany than Austria, as well.
You are in the hands of the airline if the weather is poor at Innsbruck - more than likely a divert to Munich, wait for a coach to be organised, find the coach, wait for someone who can’t find the coach etc. Worst case is the flight is cancelled and you lose your holiday.
Innsbruck is an excellent access into the Tirol but be aware of it’s limitations.