Cleaning never hurts anytime, but outdoor tarps in my neck of the woods tend to shred in the winter winds. Critters like to live under them too. While they're still intact, they have the capacity to retain condensation on the paint job. I'd rather expose mine to an occasional rain or snow, and let the wind keep it dry the rest of the time. I also question how much circulation can occur - regardless whether the mower's sitting on the ground or elevated - if the whole thing's encased in a tarp anyway (?)
Sharpening exposes fresh metal, freshly sharpened edges rust quickly when not used. I prefer to sharpen in the spring, and as required throughout the mowing season. Also during idle periods, moisture from condensation will also accumulate inside the transmission, in the U-joints, in the wheel bushings and bearings. I hold lubrication and gear oil off till spring too. The only implement I keep indoors is the three point broadcast spreader. Basically - when my implements are done for the season, I simply park them in the pasture. Getting them ready to work again is a spring thing.
If you have indoor storage, my advice is to use it. Touch up any rust spots. A tarp may keep the dust off, but it also represents an inviting home to mice - or worse. Set the mower on end if you can, it frees up floorspace and REALLY lets air get to the underside. Plus, it permits you to let the air out of the tires over winter. Leave the sharpening and lubrication go till spring.
//greg//