Squeeking noise when car starts in the morning, when it's cold.

Does the noise change or go away if you turn defrost on-which will engage the compressor-if so may be the clutch dragging.

did you adjust the idler pully, to tighten up the belt?

Check the idler pully. It might also be the water pump. The belt could be bad as well or something could be seizing up.

Look under the car for the noise.

The Antilock Brake Hydraulic Control Unit is directly under the air cleaner box. Is your Antilock Brake light coming on?

its your secondary air pump. it turns on in the cold morning to inject more air into your exhaust, something about emission. its normal to be high pitched. once on my car it was way loud, i looked and the hose had disconnected. either way its normal if its not super loud. but if its everyone is looking at me loud then check for loose hoses!

Have your power steering belt checked and adjusted, or replaced if worn.

Probably serpentine belt to loose.
It is common. Have it checked.
Also can be water or oil getting on belt and it starts slippering and makes the noise.
Good Luck

most likely your alternator, when it is cold and you start the alternator needs to recharge a heavy discharge, bearings or slip ring worn. also check the drive belt for wear,

No it is normal bicause the car is "cold". When the motor gets the working temperature the noise stop's.