I got my E89 last winter and drove an E85 for several years prior to that as my only car in rural New Hampshire.
You must have good snow tires, and I'd recommend 18" rather than 19" wheels for winter use.
I just drove back from Montreal last weekend, where it snowed (albeit lightly) for several days running. The last time I drove back from there in October it was into 2 1/2 feet of heavy wet snow in New Hampshire. Each time it handled fine. A Z4 makes a perfectly good year-round car.
The only caveat was given above: deep snow needs to be plowed first. I do have access to my wife's X3 for really deep days, but since I've had this car that hasn't been necessary. With the E85 there were a few days each winter when I'd take her car because mine had such low clearance.
2004 Z4 3.0 Sport - Being driven by son
2011 Z4 35is Atacama Yellow - Gone
2014 Z4 35is Valencia Orange
, vacation rental villa in Cozumel, Mexico