There is no way to generalize the entire USA.
This answer will quote jury instruction from Illinois. Do not generalize to elsewhere.
As a general rule, property owners have no duty to remove natural accumulations of snow, ice or melt water from their premises...There is no liability for clearing off snow under which there is a natural accumulation of ice.
Recovery for falls on icy sidewalks or parking lots can be based on negligent design or maintenance of the underlying pavement. Other cases have recognized a cause of action for negligent removal of ice and snow because an “unnatural accumulation” resulted.
Illinois courts have applied the “unnatural accumulation” requirement in a number of specific contexts. There is no duty to warn customers or invitees of the danger of natural accumulations... Property owners have no duty to clean up ice, snow or water which is tracked in by customers...or to provide mats or rugs for customers to wipe their feet. ... A mat, which becomes saturated in a store's entryway due to tracked-in water, does not transform the water into an unnatural accumulation, nor does it aggravate the water's natural accumulation. ... Where there is no evidence to show that moisture originated from an unnatural accumulation, property owners are under no duty to remove water from interior floors near mats... Normal usage of the property by vehicles or pedestrians which leaves ruts or ridges or ice in natural accumulations or which causes ice to form as a result of thawing and refreezing on an otherwise properly maintained surface has been held to be a natural accumulation.
Given that a property owner is not liable for injuries caused by natural accumulations of ice and snow, a property owner cannot be held liable for a failure to provide adequate safeguards to prevent others from falling as a result of those natural accumulations.
The existence of a municipal nuisance ordinance does not imply a duty to remove natural accumulations where the common law creates no such duty. ... A municipal ordinance requiring abutting property owners to remove snow and ice from public sidewalks within 24 hours of snowfall of two inches or more is an ordinance for the benefit of the municipality. Such an ordinance does not create a duty for the landowners.
The General Assembly adopted the Snow and Ice Removal Act (745 ILCS 75/1-75/2), effective September 14, 1979. Section 2 provides:
§2. Any owner, lessor, occupant or other person in charge of any residential property, or any agent of or other person engaged by any such party, who removes or attempts to remove snow or ice from sidewalks abutting the property shall not be liable for any personal injuries allegedly caused by the snowy or icy condition of the sidewalk resulting from his or her acts or omissions unless the alleged misconduct was willful or wanton.
A contract or a lease agreement that requires snow removal can create a duty to remove natural accumulations. ... The plaintiff has the burden of proving that the defendant knew or should have known of the dangerous condition and failed to take proper steps to guard against it. The lease may create a duty of snow removal but does not establish a strict liability standard. ... A visitor on the property is not necessarily a third-party beneficiary of a contract of the property owner with a snow removal service. [It was] held that a lease requiring the removal of “all” snow and ice would be construed as requiring removal of all that was reasonably practical and that such a lease could create a duty of ordinary care toward a business patron who fell
In 1996, the Second District considered this statute in the context of removal of snow and ice from “sidewalks abutting” residential property. In Yu [v. Kobayashi], the court found that the defendant was not liable for any negligence in removing or attempting to remove snow from a paved area between the stoop of an apartment and a parking lot where plaintiff slipped and fell. The court noted that the paved area, part of the continuous walkway, was sufficiently similar to a traditional sidewalk and to classify it otherwise would be unreasonable.
the plaintiff has the burden of proving:
First, there was an unnatural accumulation of [ice] [snow] on the [property] [land] [building] [other] which presented an unreasonable risk of harm to people on the property.
Second, the defendant knew or in the exercise of ordinary care should have known of both the condition and the risk.
Third, the defendant could reasonably expect that people on the property [would not discover or realize the danger] [or] [would fail to protect against such danger].
Fourth, the defendant was negligent ...
Fifth, the plaintiff was injured.
Sixth, the defendant's negligence was a proximate cause of the plaintiff's injury.
So basically in Illinois, if there is an unnatural accumulation of snow or ice on your property you do need to remove it (or at least not be negligent with respect to it). See the link for more information about the distinction between natural and unnatural accumulations.
If the accumulation is natural, the owner can only be liable if the underlying pavement is negligently designed or maintained, or if there is a contract requiring the owner to remove the snow. Whether or not you shovel naturally accumulated snow is not an issue. However, it is possible that by removing naturally accumulated snow you could create unnaturally accumulated snow, for example the instructions cite to "McCarthy v. Hidden Lake Vill. Condo. Assoc., 186 Ill.App.3d 752, 542 N.E.2d 868, 134 Ill.Dec. 522 (1st Dist. 1989) (negligently conducted plowing created jury issue as to unnatural accumulation)". However, the Snow and Ice Removal Act, partially quoted in the instructions, provides a specific exemption from liability for shoveling of sidewalks abutting residential properties.
The full text of the act is:
Sec. 1. It is declared to be the public policy of this State that owners and others residing in residential units be encouraged to clean the sidewalks abutting their residences of snow and ice. The General Assembly, therefore, determines that it is undesirable for any person to be found liable for damages due to his or her efforts in the removal of snow or ice from such sidewalks, except for acts which amount to clear wrongdoing, as described in Section 2 of this Act.
Sec. 2. Any owner, lessor, occupant or other person in charge of any residential property, or any agent of or other person engaged by any such party, who removes or attempts to remove snow or ice from sidewalks abutting the property shall not be liable for any personal injuries allegedly caused by the snowy or icy condition of the sidewalk resulting from his or her acts or omissions unless the alleged misconduct was willful or wanton.