Can you leave a Muskoka chair outside all winter?
Yes. Frost cracks things that have water in them. This has none.
Wood splits in winter because water in the end grain freezes and expands. Resin cracks because it goes brittle in the cold and a snow load or a knock finishes it. HDPE lumber does neither: it absorbs no water, so there is nothing inside to freeze, and it stays flexible to well below −40. The chair simply sits under the snow until April.
What to do in fall
Nothing. If you have the room, turning the chairs to face the wall keeps the seats clear of snow, which saves you brushing them in spring. Do not stack them on a slope; they are heavy and they will find the bottom.
On a dock
If the dock comes out, the chairs come off it. That is the only case where a Muskoka chair moves for winter, and it is about the dock, not the chair.
What to do in spring
Brush off the snow, hose off the pollen, sit down. If a bolt has loosened with the temperature swing, a quarter-turn.
What twenty winters do
Nothing you will notice. The colour is through the board, the UV stabiliser is through the board, and winter is the easy season for it — the sun is what ages outdoor things, and there is very little of it.
Questions
Will snow load damage it?
No. The boards are solid and an inch thick; a winter's snow on the seat is well within what the chair carries every time someone sits down.