Caveat: It doesn't freeze very often in the area my boat is stored. I don't pay any special attention to whether the motor is up or down, except after it's rained, when I'll drain the exhaust hub to limit mosquito breeding.
Usually, people recommend keeping the motor down. This prevents rainwater from collecting in the exhaust nacelle and freezing (assuming severe enough ambient conditions), which may split the LU.
Manufacturers seem to recommend either lowering the motor, or blocking the motor up and running the tilt/trim rams all the way down (as doggypaddle suggested, it retracts the rams and keeps them out of the elements.) The oil he referred to, I believe, is the hydraulic oil that drives the rams, not the engine lube oil.