The 410c board is not rated for extended temperature operation, and, as far as I know, there are no plans to create an extended temp range version of the board (someone please correct me if I am wrong). If you wanted to buy components and build your own 410c board (and do the work to qualify the board at extended temperature range) it could be possible to get down to -30C.
The Qualcomm chipset is rated down to -30C (see the datasheets under documentation). I haven’t checked the remaining components on the board, you will need to look at the critical components (HDMI transmitter, memory, usb hub, etc.). The Qualcomm chipset was not designed for, and is not available with any further extended temperature range. You will need to check with the suppliers of all of the other components on the board to ensure they are available at extended ranges.
Having said all this, I suspect that most of the boards will work at -40C, but I have not seen this tested, and it is certainly NOT guaranteed to work.
Full Disclosure: I am an employee of Qualcomm Canada, any opinions expressed by me in this or any other post may not reflect the opinions of my employer.