First, welcome to OCC......
BTW...the 682 is a Garden Tractor.
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Do I really have to run different oil in the winter than I do in the rest of the year?
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I have a KT-17 in a 784 and I follow what Kohler recommends. However, it is your tractor and you can run what ever you want.
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and do not see an oil filter. I've looked over the entire engine and don't see one.
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Not all KT-17 Series II engines have a Oil Filter. Mine don't.
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I would have thought a tractor would have a fully locked differential
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NOPE,
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I have not yet changed the transmission fluid / gear oil - should I?
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Unless you have direct knowledge and know when the last Hydro Oil Change was, then I would change it to be on the safe side. Along with the Hydro Fluid, change the Hydro Fluid Filter.
