Cotopaxi is a census-designated place and U.S. Post Office in Fremont County, Colorado, United States. The population as of the 2010 Census was 47. The Cotopaxi Post Office has the ZIP Code 81223. It was a small train stop on the Denver and Rio Grande Western Railroad along the Arkansas River. There is a small local population living in Cotopaxi, most of whom are Caucasian.