We have two of those plastic mats from Ikea to protect the parquet floor under the kids' desks (those wheelie office chairs destroy the wooden floors). But they are horrible. I guess they are static and attract all the dust which somehow creeps underneath. They protect the floor but they always look ugly dirty. I don't quite see how you could put a mat underneath one of those. Hmmm
BTW - I would NOT NOT NOT use a steam cleaner on a woven paper mat.
As for the Artek chairs, I didn't realise they were paper too. We have them (in beige) in a classroom in one of the places where I teach, but we always sit on the comfy chairs round the coffee table instead. The students said the woven chairs were Ultimate Discomfort. @raamv... why would anyone spend circa 500 euro on an Artek chair and then cover it with a 29€ cover from Ikea

? Just buy a set of chairs (and a few spares) from Ikea and spend the rest on beer.
I love Finnish Design stuff but sometimes I am really turned off by the practicalities of living with it all (not to mention the prices). Some of those lamps just collect dust... all day, every day. And I have a set of Arabia dinner plates which don't fit in my dishwasher (well, they fit but for some reason they don't get clean)

And some Iittala champagne glasses (stamped 2000 for the MIllennium) with loooong stems, from which it is impossible to drink sitting down; you have to be standing up, reasonably straight.