I'd say that because you are getting EBD failure the system thinks there's a problem with the rear wheels which affects EBD. If it thought the failure was at the front there wouldn't be EBD failure, just ABS and VDC. Either this or it thinks there's a fundamental problem with the whole ABS and is shutting down the complete system. Is the handbrake freezing on/dragging perhaps ?
Disabling EBD would not be a feature if the system "detects" snow since this would make the car a death trap to drive. I wouldn't drive without EBD working, or at least drive very carefully. This is far more critical than ABS because without it you will loose the back end in an instant should you brake abruptly. There's no mechanical rear brake pressure limiter on a 147, it relies soley on the electronic brake distribution.