I don't run fogging oil through them, just spray some of the stuff in the cylinders before storage and turn it over a little. With the 33, think I would remove the plugs and spray it some, then just turn the flywheel a couple of times by hand (clockwise), then put the plugs back in. When firing it up in the spring, will want to run out the fogging oil a bit, then clean and regap plugs (or replace).
My first step is to run the gas out of the system, then spray the the linkages with WD-40. Change out gear oil. (mixed opinion on running carbs dry, but I routinely do it -- and particularly for winter storage.)
Lower units are sometimes wrapped in plastic bags, and I've never been sure why that is -- protection from rain and snow, I'm sure (maybe critters looking for a winter home or pantry). Has always seemed to me wrapping like that would invite thawing/condensation/refreezing -- sealing in moisture as much as sealing it out. Not sure. Like to keep snow and ice off the hood, particularly if detailed -- but think tightly wrapping has the same drawback there.
(And stick it in the garage somewhere, if you can....) Haven't read that sticky yet.