Snow removal takes a lot of effort. It was easier to switch out wheeled carriages for sleighs. Sleighs work better with more snow, so that according to this article:
in the 18th and 19th centuries, "snow was never a threat" to road
travel, "but rather it was an asset."
The more densely packed snow became, the better. Some municipalities even had special "snow rollers" to compress the snow:
Some inventors did try out horse-drawn plows, but these were intended for pedestrian alleys, not thoroughfares. In the U.S., these were most popular in the "snow belt," with Milwaukee being the first major city to use one in 1862. However, horse-drawn snowplows are not able to handle blizzards, as the Blizzard of 1888 (which dropped 50 inches of snow on the East Coast) made clear:
The plow-pulling horses, like everyone else, had no choice but to stay
inside and wait for the snow to melt. Cities in the region learned a
valuable lesson about preparation, and the following year many
implemented measures like hiring more plows and giving them assigned
routes, and sending the plows out to start clearing the roads in the
early stages of the storm.
It was the introduction of automobiles that required cities to take snow removal seriously:
As automobiles replaced horses and carriages on the roads of the U.S.,
the snow problem got flipped on its head. It wouldn't be enough to
clear the alleys and pack down the snow on the main roads anymore.
Cars required dry, safe streets. Motorized salt spreaders were
introduced, but they often didn't do enough, and urban sprawl meant
most cities were just too big for horse-drawn plows to clean all the
streets. In the early 1920s, Norwegian brothers Hans and Even
Overaasen and New Yorker Carl Frink independently came up with designs
for car-mounted snow plows. These were, apparenty the perfect solution
to the modern snow problem, and the company Frink started is still
producing plows today.