Why is the clutch fan engaging when engine is cold

Because of the internal design, they engage for a short period before recognizing and adjusting to the cool temps. If you allow the engine to warm up a bit, it should prevent this from happening.

To help explain, the fan clutch is a viscous design. That means there is fluid in it which is what engages the unit and the fluid flows through a valve. The hotter the temp, the more flow. Once there is full flow, the fan is moving as fast as the engine. Now, when you turn the key off, the heat under the hood increases for a short amount of time. At that point the fluid valve opens and allows fluid to flow more. Then when you start it, the thermostatic conductor on front closes the valve because it's cold which takes a short amount of time to slow the fan. Until that happens, that is what you hear.

Does the fan eventually stop making noise?

Let me know.
Joe