I'd be looking at the battery. If the terminals are not nice and snug and preferably coated with an anti-corrosion solution, they can appear to be connected but not actually be connected enough to fire the starter.
Also, today's modern batteries are Calcuim based, which makes them lose capacity abruptly if they've ever gone flat. Typically though, the cold weather just makes the car harder to start, and the battery struggles. But you are not describing that particular case as you say there's no noise.
It is odd you don't hear a noise. Here's another possible cause:
Mercedes use a BUS system to activate various electrics. The A-class was notorious for this sudden misbehavior, see this article. Your auto mechanic may not have noticed the electronic solenoid.
I suspect the cold weather has simply caused the fault to become more evident, rather than being the cause itself.