Components are only tested to specific temperature ranges, and will likely continue to work for a reasonable amount of skew outside of those ranges. Since the BMV-712 is a solid state device, it would likely continue to monitor far below that threshold. I would expect that the display and control buttons would be the first things to fail as temperatures fall. At some point, of course, the entire device would cease to work. In my anecdotal experience, displays don't always come back from subzero temperatures, but most other solid state components will once warmed up.
The more important question here is what part of the BMV-712 is going to be exposed to such temps? The shunt, I imagine, would function perfectly fine well into the negative temperatures, which is the part that needs to be located near your batteries. The display could be located inside the camper, where additional insulation and the fact that it might be heated comes into play. In that case, I'd be much more worried about your television ceasing to work than I'd be of the BMV.
And finally, it's worth mentioning that if your batteries are inside a bay door of the camper, it's likely a little warmer than the outside temperature in there.
2000 Country Coach Magna 40',
4380W solar, 22.8kWh LiFePO4@48V, 450AH AGM@12V
2020 Jeep Wrangler Unlimited Rubicon 2.0T, cloaked on 37x13.5s