Significant battery drop/reboot, but only in cold weather (+5°C/+41°F) with camera - expected behaviour or battery defect?
All batteries achieve optimum service life if used at 20°C (68°F) or slightly below
For Li Ion ( or Li Po) the ideal charging temperature is 0°C to 45°C
(32°F to 113°F) and operating temperature is –20°C to 60°C
(–4°F to 140°F) Source


Based on the above, it looks like you have a poor battery given that


It is being operated within the designed temperature range
Unexplained sudden drop from above 50% or more to zero
Marginal increase in charge when brought indoors


Till you get a replacement battery all I can think of by way of power consumption reduction is to delay the cloud upload (do it once it's charged / WiFi)

Edit: Try a different camera app. It looks like Open Camera does consume more power and show increase in battery levels after reboot as quoted here -in particular post of 17/12/2017 which matches very closely to what OP describes. If that doesn't help much change battery