My previous association was located in Fairfax County, VA.
I went through my old files and all the snow removal contracts I have copies of does include an indemnity clause. It was for falls, accidents and lack of ingress/egress. I was on the Board for 8 years and never had an issue over falls. People complained that we weren't high enough on the contractors list to be one of the first properties plowed, but nothing concerning falls. If someone complained about ice, we would contact the contractor to make an extra salt run.
Not plowing, I think would place the Association at more risk than hiring a good contractor to remove snow from private streets.
Worst case, someone dies because an ambulance couldn't access the property due to Associations failure to plow.
I will also point out that residents need to expect ice even with sidewalks and streets plowed. Ice can cause falls. Virginia has contributory negligence clauses (i.e. did the resident use enough precaution when venturing out into the snow/ice?)
To prove fault/negligence on part of the Association, one would have to show the Association failed to take reasonable steps to address snow and ice. Reasonable steps would be to plow, salt roadway, plow again later in the day if needed, salt roadway again as needed throughout the next few days.
I offer this article from 2021:
Shoveling Out - Snow Removal Responsibilities and Liability for Community Associations