It is an AWD, the tires are Nexen 245 - 60R18 105v M&S. Not sure if those are good quality or not. The look almost brand new.
I have a feeling someone replaced the tires thinking it would fix the wandering on snow covered roads but it didn't help. They ended up just selling the vehicle instead checking more.
Could it possibly be some sensor in the AWD causing uneven power to the wheels?