The quick answer is... it depends! As previously mentioned, most modern rattan and wicker furniture is now made from plastic 'PE-rattan' or polyurethane which is waterproof, frost-resistant, and generally pretty weatherproof outdoors. However, this plastic polymer upper is given strength by a metal frame, and finding out what this frame is made from will give you a good indication of a PE-rattan patio set's long-term durability outdoors.
The most common frame options you're likely to come across are steel, powder-coated steel, or aluminium. Each of which performs quite differently outdoors, and has quite significant price differences.
The most affordable rattan patio furniture will generally be made with a steel frame. This makes for heavier furniture, and you'll want to make sure you look for powder-coated steel. This is because steel is highly corrosive when it comes in contact with water, and the frame will rust quickly outdoors if moisture reaches the metal surface. This problem is 'solved' by powder-coating the steel in a dry paint powder that's cured through an electrostatic process to form a hardwearing seal from the elements.
The downside of powder-coated steel is that if that painted surface chips then rusting can occur quite quickly, so you'll need to repair any knocks to maintain that waterproof seal. Joints and fixings which are hard to thoroughly powder-coat and open to abrasion can also become a weak point, allowing moisture to penetrate and reducing furniture's lifespan.
As such most manufacturers will recommend you store steel-framed rattan outdoor furniture in a sheltered environment during inclement weather to prolong its lifespan. This can be inconvenient if you don't have anywhere you can realistically store it that's not indoors. Plus, steel can be pretty heavy to move. A waterproof outdoor furniture cover will help to protect steel rattan furniture from the worst of the elements, although it's hard to prevent damp from penetrating over time, so expect steel-framed options to have a shorter lifespan overall.