Pedals spin freely in cold conditions
The pawls in your freehub are most likely getting stuck, causing them not to lock and transfer the force from the cassette to the wheel. In your case as the bike is new it is probably due to it being assembled with grease rather than a lighter oil, but the problem can also come with ageing. You will need to rebuild the freehub. This is not the easiest procedure and requires some specific tools (chain whip and freehub nut at least) so probably get your bike shop to do it.

The unusable gears on the back could be a number of things, rear derailleur limit screws, lack of cable tension, bent hanger/derailleur... If you are already taking it to a bike shop just ask them to fix it.

EDIT: Based on the additional information (-30 not 30  Celcius and secondhand), like others say the freehub is most likely frozen due to old grease and or water which has gotten inside the hub. Same advice still applies though, you will need to overhaul it and get new grease in there or just buy a new one.