stopping in the snow with only 2 snow tires on the front tires may cause some stability issues and the car might swap ends.
in the dry, not so much, but it still might at the limits of traction (evasive manouvers).
IMO, i would try keep all 4 tires similar. i dont think they need to be same brand. but i personally wouldnt mix summer/allseason/winter in the winter, although i might mix summer/allseason in summer if i was in a bind.
for auto-x: '04 Liquid Grey ZX3
for street: '02 Infrared SVT