A horse walking through deep snow can make snow balls around its hooves, which can slow it down or even be hazardous. Small hammer picks were often carried to remove them. Instead of plowing the snow out of the way, in the later 1800's it would be sometimes be packed down with rollers for easier travel. Thoroughbreds are finicky and don't do as well in the cold, but because most horses get thicker hair in winter (and are big animals and don't lose heat as quickly as small ones) most horses don't easily get chilled.

In some ways it could be easy travelling and pulling loads with horses and oxen in the winter because once the snow was packed down , sleds and sledges and sleighs could be used. Pulling a sledge full of logs was very practical- the sledge could be simple and sturdy and could be pulled over packed snow with little friction. Also, when trees were felled, the logs could be more easily dragged over the snow than dragged over the ground, so cutting timber was often a task for a farmer's winter months. Here's pretty good example of how horses could be used for logging in the snow.

In deep snow country people would put snowshoes on their horses. They would also change the lead horse out with others to keep them from tiring out from breaking trail for the others.