Opinion (but not from a local)Temperature -- Can be cold, but I have had some cold experiences at Vail too. Not sure what the chance of being caught in a cold spell is. Personally, I would try hit the end of Feb.
Cloudy/Sunny -- Not really sure. Remember, it takes clouds to make powder.
Wind -- Never been a problem on the lower mountain. The upper mountain can be closed due to wind, but I don't think that is too often.
Powder -- Big Sky is not known for massive snowfall. The Utah resorts can have twice as much snow. But that said, Utah resorts are known for the local powder sharks that go on a feeding frenzy when it snows and chew up the untracked really fast. Whereas BS is known for lack of crowds which means that any powder that falls lasts a lot longer.
Personally BS is one of my favorite areas: Lack of crowds, nice long fall line intermediate runs for the family, easy access to some steep terrain for me, big enough not to get bored
Hopefully some locals will chime in and give more info or even a different perspective.