From the National Endowment for the Humanities archive, a clip from the New York Sun of March 15, 1888, reporting on the market’s first day open after the two day shutdown for the Blizzard of 1888.
The paper noted that brokers “got in from their out-of-town homes, but telegraphic communications hadn’t been established with other stock speculating centers.”
In this case things really have changed. Though the telegraph was down then and cell phones are now, the electronic systems that now govern international equities markets have held up fine. Getting into Manhattan, however, has been virtually impossible (and with many offices stuck without power, irrelevant).