I cut with a chain saw all the time. If it is set up properly it will not oil the wood. The oil catches in the chip and flings off. Though it is a possibility, but the cords I go through I am not using a bow saw.
Peanut oil has worked good for me so far. I run a couple of "tanks" of it through to flush out the petroleum oil before I cut smoking wood. I haven't tried it in colder weather, but I don't have any gumming up problems with it in warm weather.