I think tyres are important, I use Goodyear Vector 4 seasons on my Red Puma, but we haven't had any real snow since I've owned a Puma.
The Thunder I used to own, didn't have the ABS or traction control working and had the popular but cheapish Toyo TR1's on the front, in the wet it used to slide all over the place, when I changed to the Goodyears it didn't. My Medium Steel blue Puma has Falken Ecorun tyres and that is fine in the wet as well.