I use a H4D-50, digital back only on my Linhof Techno in outdoor conditions. Obviously the camera is less robust than say a Canon 1D, but you don't need to worry about some occasional water drops or some light snow. I've shot in -30C (-22F) without issues, the LCD gets slow etc, just on all electronics, but it works.
If it starts to rain for real, I protect it with my umbrella, or stop shooting.
I don't know much about the batteries as when I use the back I use an external battery. But there is no reason to believe that there would be issues at 40F, which is above freezing. The camera is made in Sweden and tested in Swedish conditions, so it's fine for cold weather.