My Fuji X-E3 and my old Olympus Pen worked at -30C.
This is my standard reply:
32F/0C isn't cold at all. You'll have no trouble apart from condensation (see below).
Down to -20C (a little below zero F) I've not had much trouble on several skiing trips to Arctic Finland or high Norway at least for the several hours I can enjoy at that temperature.
The camera will be warm when you take it out of your accommodation (unless it is a tent or snow hole).
It will slowly cool but won't condense while outside.
If you put it back in your pocket it will condense (warm and moist in your clothing, camera has cooled), so it needs to be in a sealed plastic bag if you do that. I've had that in the UK this autumn - cool, wet day, Goretex type jacket (which works badly in warm wet conditions, so a bit, ahem, moist inside - the pockets are inside the coat to keep the stuff therein dry), OK going into the pocket, misty coming out.
My advice is to keep the camera in a ziplock bag in a coat pocket, inside out layer if possible and take it out to shoot, then back in the bag and then in the pocket. I've taken several film SLRs, compacts and mirrorless out in -20 and they've carried on working for several hours. The main component that suffers is the battery and that is fairly immune to condensing so you could keep a spare one warm or re warm the main one in an inner pocket.
Going back inside I leave mine in the plastic bag for several hours to warm up slowly. I've debated the how long should you leave it before getting it out again but still think 10 minutes (which some people suggest) is far too short a time. It depends on how cold it got and the humidity in the room you take it out in. I'd definately wait hours at room temp before taking a lens off. Huts selling hot drinks are always VERY humid!
Skiing I generally don't have a computer so there is no point in getting the camera out to unload the shots, I generally simply recharge the battery before I go to bed.
The real problem is going somewhere warm and moist on holiday. You leave cool air-con into warm and moist and the camera steams up just when you want to use it.
https://www.ritzcamera.com/static?id=articles/tips/winter-photo.html
So the GR should be OK, not sure about the X-A1. Why not pop it in the freezer and see? That is about -15C.
Edit: You gear list says X-E5. Take that plus a warm battery but you absolutely MUST have it in a bag when you go indoors, into a car, bus, plane, hut, tent etc. They will be moist from melting snow and a cold camera will condense. DO NOT change the lens in condensing conditions, condensation on the sensor will leave water marks and need a wet clean. I've swapped lenses outdoors in the cold but never in the warm if the camera is cool.
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Andrew Skinner