According to The Field Museum's Genghis Khan online exhibit...
Leather, 19th-20th century, National Museum of Mongolia
These centuries-old leather boots are like those worn by warriors in Genghis Khan’s empire and nomadic Mongolians today.
For battle, these felt-lined leather boots were often covered with armor plates as well. The turned-up toes signify respect for the land by minimizing the mark they left on the ground.
While the boots in the exhibit are not 13th century, the exhibit states they are of a similar style. The leather would likely have come from cattle or yak. So yes, "cowhide".
(As a side note, Discover Mongolia offers a different explaination for the upturned toes: "it's also true that boots are so thick and rigid that if they were flat, they would be almost impossible to walk in.")
Here's a Mongolian tanner describing the process of making traditional leather.