Well, I thought I would revive this thread because there is so much useful information and it occurred almost exactly a year ago in winter. I ran into the same problem with my Stihl 036. The saw was being stored for about a year in the garage and we have had some very cold January weather. I decided to service the saw, which was showing some oil leakage on the storage shelf. It had only about 1/4 tank left. I started the saw, still a bit cold, ran it awhile, tuned it a little, and then cleaned it up for a Pic to post here.
After letting it sit for two hours, I noticed a leak, raised it up above a drip pan with a block of wood and let it sit overnight in the shop at room temp. Next morning the pan was full of bar oil and the engine had leaked almost all of it out. I removed the bar and chain, removed the thin steel inner plate, cleaned things up, and noticed the oil tank vent hole was threaded for M4 but no screw was there. I installed a short M4 screw in that hole and waited. Drips stopped.
Next I filled the tank with fresh oil and watched some more. No drips. I reassembled everything, including the bar and chain, started the saw and ran it. Oiler was working fine. Then I took the saw and put it back above the drip pan and let it sit overnight. Next morning not a drop had dropped. I started the saw again to make sure I was still getting oil to the bar, and it was working flawlessly. Now is it possible that the short M4 screw I installed was the cure? Frankly, I'm not even sure that this threaded hole was a tank vent.