On the East Coast of Canada - where it gets very cold in the winter - the options are:
1/ to leave the outboard down so that the thermal mass of the water circulating around the lower end, and the reduction in cold wind on the lower end and the internal cooling tube with water in it - doesn't freeze and block circulating water - or
2/ pull the boat,
On the West Coast - it rarely gets that cold most places, most winters - so those above realities are not really an issue.
The issues on the west coast are more likely:
1/ logs catching your bottom end in the tide, wind and river currents - esp in areas with intensive logging and/or intensive log booming/shipping, and/or
2/ poor mooring skills and bad mooring lines combined with heavy winds & chop leading to your lines chaffing off and your boat floating away in the middle of the night. Then your boat usually finds a beach - most often a rocky one where your bottom end gets knocked off because it was in the down position.
So, the better option is to pull your boat for long-term storage - or put your bottom end up for shorter moorage periods to avoid a couple common tragedies.
Then there is the issue of rain and rain filling your boat up and sinking it at the dock....