What's a good approach then? Cover on and surround it with critter repellent?
Your tent/shed is better than parked on an un-roofed back patio over your long, wet winters. I wouldn't leave the tires on the dirt for that long, a sturdy-enough sheet of plywood will help.
A waterproof, breathable cover is an excellent suggestion also. I found covers for mine at a local shop years back that have worked fine. They fit over the top box and windshield and strap to the tires close to the ground. Bought both to fit the ST1300 so they work well on the ST1100 also. Sorry...no company tag on them. I've had to leave the bikes on the back porch for extended periods (weeks) several times while working on other vehicles....and plumbing.... and needed the garage so the covers came in handy. Long way of saying you can find a cover that will fit for a decent price, start shopping Amazon and see what's available.
Might want to remove the battery if it isn't easy to use a battery tender of some sort. Your harsh winters are with you longer than down south.
Add a some fuel moisture absorber such as Seafoam to prevent moisture damage (rust) in your fuel system. Full tank of gas to limit the opportunity for moisture to intrude.
When you roll it out in the Spring, look under the plastic bodywork for evidence a rodent made the bike a home...usually between the tank and top of the engine. Might want to consider some method of mouse/squirrel deterrent.