While humans can get cholera from water infected with Vibrio cholerae, horses do not. The water supply was still fit for livestock and the boilers on the steam engines. Season 3 takes place in 1867, five years after Louis Pasteur confirmed that boiling water for a period of time could kill bacteria in drinking water. This information would have been significant for both urban and frontier communities, though would have been much slower to reach the latter.
The mortality rate for cholera at the time was 50-60 percent.