Loud fan when starting?

This can happen in cold weather because the fluid inside the clutch fan is more solid and forces the clutch fan to lock up and then loosen up to normal once the temperature is higher, but if you have never heard this noise before even in cold weather the clutch fan should be replaced. Here is the location of the fan and how to change it out. Check out the images (below). Please upload videos in your response of any problems so we can see what to help you with.

What was the temperature outside? If it was cold that could be the clutch on the cooling fan. They have a fluid inside them that reacts to temperature. When it is cold it gets stiff and needs to warm up a bit to free up. Usually that doesn't take very long because the shearing forces in the clutch generates heat fast. So, you might have heard the woosh of the fan for a few seconds and then it started freeing up. I might suggest having someone stand where they can see the fan with the hood open when you start it the next time in similar conditions. See if the fan spins up very fast, then stops making noise.

Yeah that sounds like the fan clutch doing what they do. Once they warm up even a little bit the tend to become quiet again. Until the engine heats up then the fluid expands and the fan will start to engage until it gets hotter where it engages fully.