The rubber in high performance summer tires is made to provide traction above 50°. Below 50° the rubber hardens and does not grip the road, this creates a loss of traction. If you don't have traction it only takes one wrong move to make you skid/slide, and crash.
And we all now that a crash = cash and time away from your Boxster.
The rubber in winter tires won't freeze or harden and will provide you with traction. At the very least you need a decent set of all-seasons. Mike.Focke totaled his Boxster driving below 45° without winter tires. It's worth the money, don't skimp on safety.
http://mike.focke.googlepages.com/theboxsterinwinter