Yes, many outdoor benches can stay outside all winter, but whether yours should depends on the material and how harsh your winters get. Snow itself is not always the problem. Moisture, freeze-thaw cycles, and poor drainage do most of the damage.
If your bench is made of teak, cedar, powder-coated metal, or poly lumber, it can usually handle snow as long as it is in good condition. Teak and cedar are naturally weather-resistant. Powder-coated aluminum or steel resists rust until the coating gets scratched. Poly lumber does not absorb water, so it will not crack or rot from freezing.
Even tough materials benefit from a few precautions. Keep the bench off direct soil or grass so moisture does not wick up into the legs. Remove any cushions and store them indoors because they will get moldy. Brush off heavy snow after storms so extra weight and ice do not stress the joints. If possible, use a breathable cover rather than a plastic tarp, which can trap condensation and cause rust or mildew.
Bring the bench inside or store it in a shed or garage if it is made of untreated softwood, wicker, rattan, or has a delicate finish. Also bring it inside if you see cracks, peeling paint, or exposed wood, since water can freeze inside those splits and make them worse. If you live somewhere with repeated heavy snow, ice, or very wet winters, indoor storage is the safer choice.
If you do not have a shed or garage, move the bench to a covered porch, against the house, or under an eave. If it must stay fully exposed, wipe it dry before a freeze and touch up any scratches with paint or sealant. A little protection can add years to the life of an outdoor bench.