Hi Linnea,
Salix babylonica is hardy to
zone 2, so it should live for you.
willows usually root easily in moist soil, but in your
zone the cuttings may not have had time to root. You may just have to wait and see if they rooted.
http://hort.ifas.ufl.edu/trees/SALSPPA.pdfThe root system of these trees will get huge and extend way beyond the drip line of the mature crown, so be sure to plant at least 100 feet from a building, sidewalk or driveway. They also drop alot of litter, so that's a consideration as well.
Newt