Sure you can run it all Winter long, as long as you have snow tires, and don't encounter anything deep. the "belly Pan" under the Z4 turns it into a Toboggan if it bottoms out, but otherwise no issues. Lots of folks [me included] have our beloved Z4 as our only transportation all year round.
2007 E81 - 120d Limited Sport Ed
2009 E89 - sDrive3.0