Pinnstol is ‘Windsor chair’. Pinne is ‘peg’ or ‘stick’, a common Germanic word of unknown origin – the English relative is pin. Stol is ‘chair’, also a common Germanic word, German Stuhl, English stool, related to Swedish stå, English stand, German stehen etc from Germanic *standan, going back to the Indoeuropean root *sta- , ‘to stand’.
A Windsor chair according to Wikipedia is “a chair built with a solid wooden seat into which the chair-back and legs are dowelled, or pushed into drilled holes, in contrast to standard chairs, where the back legs and the uprights of the back are continuous.” It is of course named after Windsor, the royal seat.
Chair comes from Old French chaiere, ‘chair’ from Latin cathedra, ‘seat’, from Greek kathedra from kata ‘down’ and hedra ‘seat’, ‘base’, ‘chair’, ‘face of a geometric solid’, from the Indoeuropean root *sed- ‘to sit’. (Greek h often corresponds to our s, e.g. i hexa- 'six', helios 'sun')