I assume schools would shut down? What about other businesses? Was there a municipal system in place to clear snow or was it a volunteer effort? How dangerous was it, would a snowstorm often have a death toll?
I'll do my best to answer your question from the perspective of New York City. New Yorkers were used to heavy snowstorms by the early 1800s, as there had been several severe winters during the 18th Century, which stopped mail service and shipping for months. During these storms, the city had ground to a standstill and people holed up in their residences; when they did brave the cold and snow to go somewhere, they would usually travel by foot, isolating the city from Brooklyn, New Jersey and upper Manhattan. Often, those sequestered in their homes would mix their refuse in with the snow, which would then flow into the streets and rivers when it melted. Those who went outside without proper clothing ran the risk of getting disoriented and freezing to death; however, the biggest casualties were horses and livestock, whose bodies were piled up amid the snow drifts.
Merchants and residents were expected to clear the road in front of their buildings (more well-off folks and important businesses would hire people to do this for them) but there was no large-scale effort to clear the streets, leading to some pretty terrible conditions. What was cleared was often dumped by wagon in abandoned lots or even in front of others’ houses. In January 1805 the city and surrounding area was hit by a tremendous storm, and it snowed for 48 hours straight. In January 1821 the Hudson and East Rivers froze over, and several intrepid businessmen established taverns in the middle of the river to service revelers. The rivers froze again in December 1835, when a gas pipe burst and started a tremendous fire that consumed seventeen city blocks that contained all of the colonial-era residences that had survived the 1776 fire; the wind chill was negative 17˚ and firefighters had to cut holes in the ice to get water to battle the flames.
By midcentury, people began fixing runners to their wagons, allowing horses to pull them even when it snowed heavily. Surface railroads were heavily impacted when it snowed badly, one of the reasons why the Elevated trains were eventually built. In 1861, the New York Times published the first weather forecast and the U.S. Weather Service was established in 1870 to record and predict weather patterns (it could only predict storms about 24 hours beforehand and had a notoriously poor record, especially in its early years).
The most legendary of storms, and arguably the one that had the greatest impact on the city was the Great Blizzard of 1888, which unexpectedly descended on the area in March of that year; the forecast the day the storm hit called for rain and brisk winds. In the years leading up to the storm, massive telephone poles were erected, holding dozens of wires each. In addition to stopping all surface transit (including stranding trains over the Brooklyn Bridge and overwhelming Grand Central Depot), wrecking hundreds of ships and halting road traffic for a week, the heavy snow pulled down the telephone poles, crippling communication and plunging newly electrified homes and businesses into the dark. 400 people across the now-Metropolitan region and New England were killed; those that were had ventured out into the cold and gotten overwhelmed, buried beneath snow drifts. After the city dug out from the gigantic snow drifts (30 to 40 feet high in some places), the city began provisioning to put the wires underground, and started planning how they could build an underground rapid transit line.
