How do you know it was a slip and fall on snow and ice? Maybe it was due to a defect in the sidewalk. If you live in the City of New York, the New York City Administrative Code passes liability on to you only if you're an owner of a commercial property or a residential property that is more than a two-family dwelling.
If it's just a one-family dwelling, then unless you made some sort of "special use" of the sidewalk, such as having your driveway cross it or planting a tree whose roots lifted up a flagstone, or unless you shoveled negligently leaving it icier than it was before you touched it, you would not be responsible.
That still doesn't change the fact that you may be sued, so fax a copy of the letter to your insurance company and, if you have one, your broker, IMMEDIATELY, so when the axe falls, they hire you a lawyer. You can't be worried that your rates are going to go up. This is why you have insurance (if you have insurance).
If you don't have insurance, you should consider hiring a lawyer. I can possibly help, as my office is located in Manhattan, so feel free to call or e-mail me.
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