If you see a pet in distress, report it. If you're in NYC and you see an animal without adequate shelter, food or water, please call 311. If you see animal cruelty in progress, call 911. Those outside of NYC should contact their local law enforcement or animal control, depending on the municipality.
As Dodo commenter Ana Luisa Luque M pointed out (thanks!), you can help animals who don't have a home by setting out sturdy boxes. (Lining a box with straw or shredded newspaper is preferred in lieu of blankets, which can freeze once wet.) And even when staggering amounts of snow aren't falling, it's worth remembering that dogs need a hand dealing with extreme cold, too.