I'm paying $175 a month for outside. If I could get covered for slightly more, I'd do that. A few hundred for a cover every 3 or 4 years should make the extra for covered storage a wash.
Rodent prevention is the biggest worry other than freezing pipes. Seal up any place they can get in with expanding foam and use Sniff 'n Stop or Fresh Cab to drive them away. These products overwhelm their sense of smell and if they can't smell predators they leave.
Don't forgot to winterize the outside shower tap and blow air through the city water check valve.