shutting down for winter?

With an AGM battery, that is fully charged, should be fine if disconnected for 4 or 5 months in cold weather.

Steps:
Disconnect the PV input to the charge controller
Disconnect the + & - cables at the battery.

in the spring - just reverse the steps, the battery will boot the charge controller ( but verify it starts up properly ) and then the PV panels when connected, will start charging the battery.

Ideally you should have disconnect switches installed at the two locations mentioned above so you don't leave anything hanging
(only need to switch the + cable)

I'd feel uncomfortable leaving batteries up there for the winter. I'd take the battery home and place it on a 1 amp trickle charger. My batteries have usually died when I leave them in.

Normally its some sort of parasitic draw. I have a shunt that is before the battery shutoff switch, and it is low amps 5 ma, but over the course of two months took my batteries down to what I think was 70%, but was still full. If you leave it in, make sure everything is really disconnected and nothing hiding.

For the panel and however its mounted, can it take all the snow you'll get?

Panels are mounted pole top and tilted straight for snow

The biggest hassle with winter in a remote camp in Maine is theft from snowmobilers. Sad to say I knew more than few folks over the years whose cabins got raided in the winter. Unless the cabin is in the ocean, frozen lakes and rivers open up easy access. Ideally haul out all the electronics. Panels will probably survive as I dont think there is an active market, although copper thieves may grab any heavy gauge wire or copper propane tubing. Wood stoves used to be popular but I think the interest has gone way down. Keep in mind how deep snow can get, with drifting what was not easy to get to may be easy to get to with deep snow on the ground. I have snowshoed up the ridgepole once or twice long ago on friends camps during heavy snow years. BTW if the camp is new to you make sure you do not need to brace the roof. Many older camps would come with a set of brace poles stored underneath the building that were installed in the fall prior to winter. They usually ran from the floor to the ridgepole. It saved the hassle of heading in on occasion over the winter to shovel the snow off the roof. A modern roof is most likely rated for 40 PSF ground snow load, older camp roofs may be far less. 40 PSF is good for about 4' of snow, head into inland Maine and that load could be exceeded. Up in Northern NH the town next to me requires 110 PSF . Usually roofs fail due to details like toenailing the roof rafter tails into the walls. There should be tie straps but a typical camp build skips a lot of details and that is what lets loose under heavy snow load.

Great advice, been at camp a few years now, it is on a lake island in Northern Maine. Was up last weekend pulling dock and getting ready.. and installing snow pole as always!