Short answer: yes, a wooden park bench can warp or crack if left out in the snow all winter, but it is not guaranteed. The real question is what kind of wood you are dealing with, how the bench is built, and whether any moisture can drain away. I have seen cheap pine benches develop deep splits after one hard winter, while a well-sealed cedar or teak bench can sit under snow for years and still look decent.
Snow itself is not the main enemy. The problem is the melt-freeze cycle. Snow lands on the wood, begins to melt during the day, and water soaks into the grain and end grain. At night, the temperature drops and that water freezes. Because water expands when it freezes, it pushes against the wood fibers from the inside. Do that dozens of times over a winter, and small checks start to form. Those small checks widen into cracks, especially at the ends of boards and around screws, bolts, or joints where movement is restricted.
Warping happens a little differently. Wood absorbs moisture unevenly. The top of a slat may get wet while the underside stays drier, or one end may sit in standing snow while the other end is exposed to wind. When one part of a board swells more than another, the board can cup, twist, or bow. If the fasteners hold the board too tightly, the stress may release as a split instead of a bend.
The type of wood matters a lot. Dense, oily hardwoods such as teak, ipe, and white oak resist water absorption better than softwoods. Cedar and redwood are also solid choices because they contain natural oils and are more dimensionally stable. Pressure-treated pine is common for park benches and resists rot, but it can still crack as it dries if it is not sealed. Cheap untreated pine, fir, or plywood benches are the most likely to warp, crack, or rot after one or two winters.
Construction and finish play a role too. A bench with slatted seat and back panels drains better than one with wide solid boards that hold puddles. End grain is the biggest entry point for water, so boards with sealed or painted ends usually hold up better. Hardware should be stainless steel or coated so it does not rust and stain the wood.
If you want to keep a wooden park bench outside all winter, do a few things in fall. Clean off dirt, leaves, and bird droppings. Let the wood dry completely. Apply a penetrating exterior wood sealer, decking oil, or teak oil, and pay extra attention to the end grain. Tighten any loose screws or bolts, but do not over-tighten because wood needs room to expand and contract. If you can, move the bench onto pavers, gravel, or blocks so the legs are not sitting in mud or standing water. A breathable cover can help reduce exposure, but avoid wrapping it tightly in plastic. Plastic covers trap condensation and can cause mildew, rot, and worse cracking when temperatures change. If heavy snow piles up, brushing it off once in a while is helpful, but you do not need to keep the bench completely snow-free.
So yes, a wooden park bench can warp or crack in the snow all winter. But if the bench is made from the right wood, has good drainage, and gets a basic seal before the first snowfall, it can survive many winters with only normal wear. The benches that fail are usually the ones that were already untreated, sitting in water, or poorly built before the snow even arrived.