Can I Place on Orbi satellite in an unheated room?

According to the user manual, the operating temperature is 32º to 104ºF (0° to 40°C) and 90% maximum relative humidity, noncondensing. This seems to apply to all (home) models of indoor Orbi routers and satellites.

The outdoor model (i.e., RBS50Y) says operating temperature is 4°F to 122°F (–20°C to 50°C), so a much larger operating range, and still 90% maximum relative humidity, noncondensing.

You said you have the RBS50, but whether there's a 'Y' at the end of the model number indicates whether it's the indoor or outdoor version. You may also be able to tell by looking at the back of the satellite. The outdoor model has vents and places for attaching mounting hardware on the back, whereas the indoor model basically looks like an egg on the front and back, other than the ethernet and power ports at the bottom of the back.

I don't know how cold it gets in the NH mountains (pretty cold, I imagine), and I don't know what the negative consequences of using it outside its operating parameters would be. Depending on your needs and usage, if all else fails, you could just store it inside the house, and only take it out to the garage periodically. Plug it in, let it sync with the router, update car firmware or whatever it is you're doing, and then bring it back in the house when you're done. PITA, but it probably gets you around the operating temperature limitations, since it would only be temporary.

Indoor Orbi manual (tech specs on pp 155, 159): http://www.downloads.netgear.com/files/GDC/RBK50/Orbi_UM_EN.pdf 

Outdoor (tech specs p 28, image p 6): http://www.downloads.netgear.com/files/GDC/RBS50Y/RBS50Y_UM_EN.pdf