Don’t even ask me how I fell down this rabbit hole in the middle of August but I was trying to understand the legal requirements in Wisconsin and other states concerning shoveling snow off the city sidewalk in front of your house. It turns out there’s no state law requiring this (though there are city ordinances in Madison and Milwaukee to this effect.)
More: there’s a 1956 Wisconsin Supreme Court case, Walley v. Patake, which holds that a property owner isn’t liable if they fail to shovel the sidewalk abutting their property, and someone falls there and is injured, as long as the snow and ice is “natural accumulation” — that is, it’s a different story if there’s a huge heap of ice on the sidewalk because you piled it there when you shoveled your driveway. In Hagerty v. Village of Bruce (1978) the Wisco Supremes clarified that even when the landowner is violating a city law by not shoveling, they still don’t take on liability. The theory here is that the liability for injury on a public walkway belongs to the city, and the city can’t delegate it; the point of the shoveling law is to require landowners to act so as to make injuries less likely, but that’s all; the city is still liable.
In Ohio (Brinkman v. Ross, 1993) you are not even liable when someone slips on the ice on your own property, as long as it’s natural accumulation. I wonder to what extent this is the case in other states? I wonder if there’s a law professor somewhere in America who’s an expert on icy sidewalk liability?
Quomodocumque 
To my UK ears, a law requiring me to shovel snow either on my property or near to it sounds very foreign. What happens if you go away for a month in the winter – do you have to make sure someone is taking care of it? What happens if you own a property which you rent out to a tenant – does the requirement fall on you or on the tenant?
If you go away for a month, yes, you have to ask a neighbor to take care of it. As for renters, leases usually specify that the tenant is responsible for the fine if the sidewalk isn’t shoveled. If the lease didn’t have that clause, I think the landlord would be on the hook for the fine.
On a visit to London in 2010 I found the sidewalks very icy and treacherous; I had to walk slowly, and elderly people couldn’t get out at all. It was explained to me that if you don’t shovel the snow you aren’t liable for any injuries, but if you do shovel it and someone falls because of some ice you left, then you are. In the U.S. (certainly in Boston, which is the only snowy place where I’ve lived) people do shovel the snow, so the liability must be limited.