Now that you've got a gorgeous new cowhide rug for your home - you need to keep it clean; and care for it the way you would any other home accessory. While they are a super-durable rug (that adds TONS of style to any interior, we might mention) genuine cowhide hair-on-hides need to be cared for.
If you fold your cowhide rug - this is fine; as it's a durable natural skin/hide. However, to get the creases out, you should simply let the cowhide lay flat for a few days - and the creases should resolve. If you need to, place a few weights (like books, or heavy, flat items) on the creases to help them flatten out.
One thing you can do to protect against stains - is visit a shoe repair shop or cobbler - and ask if you can purchase some suede waterproofing spray, and confirm beforehand whether it will effect your hide's natural color scheme. This should be a safe protection for most light colored hides, but either way - confirm that it won't discolor your natural hide coloration. This will help protect your cowhide rug against stains, before they occur.
It's also safe to vacuum your cowhide; or take it outside and shake it off. Sometimes - if there's an odor associated with your rug, you can also let it air outside.
Here's to a long, lovely life for your cowhide rug.