You can use a power bank to charge the phone and controller.
While we don't have to fly generally in that sort of cold here (Australia), I would have thought the phone should be a bit more resistant to low temps than that though.
You have it set up to not charge the controller while connected ?
This may be why the phone drained so fast, and controller was still ok (not a bad thing in that scenario, I guess).
You couldn't recharge the phone at all while the lightning connector was in use flying.
I'm not sure you can use the powerbank on the controller usb micro-a at same time as usb-a connection to the controller.
My M1P has both controller points, I use the usb-a to ipad to fly, not tried the usb micro-a (for anything but the phone connection early on), as my controller usually lasts at least 4 - 5 drone batteries of flying.
From memory reading here, both outlets on the controller can't be used same time when connected to the drone, so you will likely have to recharge controller and / or phone between flights.
Not too hard when moving around by car to different locations etc, but when you say you want to use a powerbank, it sort of indicates you want to do this recharging in the field while away from regular charging sources.
If you can't charge while using the controller flying, it might be inconvenient given the cold and time it would take not being able to use the devices.
