A 360 camera has no crop to hide behind, so whatever the winter sky is doing at 3 pm, every scene shot that afternoon will show it. Winter does not make a good tour impossible, it just moves the decisions earlier in the day and adds two problems a summer shoot never has.
Short days mean a tighter shot list
Useful daylight in the depths of winter can run out by mid-afternoon at higher latitudes, and a 360 camera facing a window captures the sky as readily as the room. Shoot exterior-facing scenes, the garden facade, the balcony, the entrance, first while there is still even light outside, and save interior rooms with small or north-facing windows for whatever light is left. Walk the shot list in your head before you arrive, not between scenes.
Low sun creates a glare problem indoors
A low winter sun sits almost level with ground-floor windows for hours, not minutes, which means it can blow out a whole wall of a panorama in a way a summer sun overhead rarely does. Angle the shot so the camera is not staring straight down the sun's path through a window where possible, and lean on your camera's HDR capture mode to hold both the bright window and the dim room in the same exposure, the same habit covered in lighting a room for 360 capture.
Snow glare does the opposite of what it looks like
Snow outside a window reflects so much light that a camera's metering often under-exposes the room to compensate, leaving the interior darker than it would be on a plain grey day. If the garden or street is snow-covered, expect to need more exposure compensation indoors than the camera's auto setting gives you, and check the preview on the camera's screen before moving to the next scene rather than finding out back at the laptop.
Exteriors want the clearing, not the storm
A freshly snow-covered garden shot in flat, even light right after a snowfall, before salt and footprints appear, is one of the few cases where winter helps a listing rather than hurting it. Shoot exteriors in the hour or two after the sky clears, not during the snowfall itself, when visibility and contrast are both at their worst.
The upside
None of this changes the publish step. A winter shoot takes the same twenty-odd minutes and uploads to Pano exactly like a summer one; the only extra cost is checking the exposure on-camera a little more carefully before moving on. A tour published in December still shows the layout buyers are deciding on, which matters more in the slow season than any other.