Hey, Barbara -
This is off the top of my head, so I don't have dates or models for you, just some basic information on American guns (I don't know what kind of revolvers were in use in Europe during this period). But you can probably get more specific info with a quick Google search.
The short answer is yes. The click would have been audible several feet away, depending on the noise level of the surroundings. On a quiet day, you might be able to hear it from as far as twenty feet away unless the guy cocking it was trying to be stealthy. And the sound of a firearm being cocked is very distinctive--it doesn't sound like anything else.
The revolvers of the 1850s and '60s were mostly cap-and-ball type revolvers; six shots powder and ball were loaded into the front of the cylinder, with six mercury fulminate blasting caps stuck on nipples on the back. Each time the hammer fell, it would strike one of the caps, igniting the powder in one chamber and firing one ball. The user would then have to cock the hammer again before he could fire another shot.
Revolvers with self-contained metal cartridges (the type we see in Westerns) did not become common until the late 1860s or early 1870s, I believe.
Hope it helps.
HN