If you're planning on installing 20's for the summer then yes definately you need a second set for the winter! The oem 20's are a strict summer performance tire. Absolutely not recommended for winter driving. I know from experience and you WILL slide all over the place even with a touch of snow! Keep the 19's with some winter tires on them such as the Pirelli Scorpions. No you don't need chains. I live in snow country and have never had to use chains even in a snow storm. There is a day and night difference when you throw on the winter tires...

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2008 X5 4.8i - Jet Black / Black Nevada Leather / Specs: Every possible factory option