It's a Haldex system in the 4motion, right? Same as Audi, so here's the spec from the owners manual:
Audi - As published in their vehicle owner's manual, "rolling radius of all 4 tires must remain the same" or within 4/32-inch of each other in remaining tread depth.
But it reality you wouldn't wanna go with that much difference with winter tires, so I'd say stick with a max of 2/32's which shouldn't be hard to find. The X-ice 3's that I picked up used for the GF's 323i were within 1/32.
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