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Who owns the road and as it sounds like it is not you do you have a registered right of way over the road to access your cottage?
Then it is not your responsibility to maintain this road. The owner is responsible and only the owner must answer to the city.
The owner is responsible for ensuring your right of way is not impeded by snow or anything else.
You can plow if the access is blocked but you can have the owner reimburse you for the cost.
I don't have any information you can print off unfortunately. I could not readily find anything when I did a quick search.