Honestly, the short answer is most outdoor park benches can stay outside all winter, but whether you should cover it depends on what the bench is made of and how long you want it to last.
If you have a bench made from teak, cedar, powder-coated steel, aluminum, or recycled poly lumber, it is designed to handle rain, snow, and temperature swings. These materials resist moisture, rust, and cracking much better than cheap pine or untreated wood. I have had a poly lumber bench outside through several harsh winters with no cover, and it still looks almost new. A quality wooden bench, especially teak or cedar, can also survive uncovered, though it may develop a gray patina over time.
That said, covering is still a smart move if you want to reduce maintenance and keep the bench looking fresh. Snow itself is not the main enemy. The real problem is the freeze-thaw cycle. When snow melts into joints or tiny cracks and then refreezes, it expands and can cause splitting, warping, or loosening. A breathable furniture cover keeps most of that moisture off the surface while still allowing air to circulate. Just avoid wrapping the bench tightly in a plastic tarp. Plastic traps condensation against the wood or metal, which can lead to mold, rust, or rot. If you use a tarp, leave an air gap underneath so moisture can escape.
If you decide not to cover the bench, at least do a few simple things before winter. Clean it well, tighten any bolts, and apply a fresh coat of oil or sealant to wood benches if the manufacturer recommends it. After snowstorms, brush off heavy snow so it does not sit and soak into joints for weeks. If possible, place the bench on a dry surface or slightly elevate it so the legs are not standing in frozen slush.
Cushions are a completely different story. Always store cushions indoors or in a dry shed because they hold moisture and will mildew quickly.
So do you need to cover it? Not always. A high-quality outdoor bench can handle one winter uncovered without falling apart. But if the bench is valuable to you, an inexpensive breathable cover is cheap insurance. For untreated wood, indoor furniture, or benches that already have cracks, covering or storing the bench is the safer choice.