Only one way to find out
Which tires did you get? Off-road / Stock 18s, 20s?
I'm not too familiar with QT 1. I guess that is considered "stock" AWD. I think someone said it's a 60/40 split front/rear, should be roughly equivalent to "Auto" on the QT 2 / QD 2 systems? Someone more knowledgable will chime in I'm sure.
Which means you should be able to go through a lot of snow, then a lot more with some good snow rubber.