A 2005 BMW X3 owner recently asked a good question about two top-tier tires on the winter tire market today.
"I'm ready to order a set of snow tires and have narrowed the search down to the Michelin Pilot Alpin PA3 and the X-Ice Xi2. Which is likely to offer superior performance on ice, slick roads, and deep snow? I don't mind paying the higher price for the PA3, but from the descriptions I have the impression that the Xi2 might be the safer choice."
Both the Michelin X-Ice Xi2 (below left) and the Michelin Pilot Alpin PA3 (below right) are great tires but designed for a different element of winter. For the conditions you are describing the Michelin X-Ice Xi2 is the best option. You will give up a little handling vs. the Michelin Pilot Alpin PA3 but gain extra traction for the deep snow and ice.