Snow removal statutes and ordinances are usually characterized as exercises of the police power, although sometimes they are upheld under the power to tax. Most states do uphold them. They previously were not allowed by Illinois courts, but in 1979 the Illinois Supreme Court reversed its position and came in line with the large majority of states. I believe that New Hampshire continues not to allow ordinances of this kind.
American Law Reports commented on the issue raised by the OP in a 1929 report on “Constitutionality of statute or ordinance imposing upon abutting owners or occupants duty in respect of care or condition of street or highway”:
“These statutes and ordinances under consideration seem to require certain persons to perform labor for the benefit of the public without compensation, merely because they are so situated that they can perform the work more conveniently than anybody else, and to require them to do it is a convenient way of distributing a public burden and causing it to be performed. Such ordinances are difficult, if not impossible, to classify. In some features they resemble special assessments, the burden being imposed in the form of labor rather than of money, but as special assessments they would be unconstitutional, because not levied in proportion to benefit. On the other hand, it seems hardly possible to require a man, as an exercise of the police power, to remedy a condition which he has not caused, merely because to do so would enhance the public convenience. 19 R. C. L. 868. Yet, as will be seen under the sections following, the ground usually assigned for the exercise of this legislative authority is the police power, although in a few cases it is held that legislation of the kind under consideration is a valid exercise of the power of taxation.”