Front squeaking noise on cold start........
 

I got a 04 4.4i and the water pump died on me a few months back and I replaced that and also replaced the deflector pulley while I was there except the main tensioner as I had to order it so postponed on doing that one. AC side tensioner and belts all looked good. Anyways during morning cold starts Im getting a squealing sound but goes away once the engine is warmed up? I replaced the main tensioner just yesterday hoping that would resolve the issue to find out it still persists. Could it be the belts? Or Alternator Bearing?

First suspect is a loose belt. You can adjust the belt tensioners to increase or decrease the amount of tension (you want more). Try a spray bottle with a little water to identify which belt it is (if it's a belt).

The rubber gets harder in cold weather. Maybe some oil dropped on it, etc.

Check the fluid level in the power steering pump. I had a slow leak that cause a squeal esp when the temps started to dip.

I know when the water pump failed alot of water went onto the belt didnt think that would cause the belt to go bad though. Will try water later today.

As for adjusting the tensioner? These are self adjusting not the manual type so theres really no way to adjust these?

Its not the power steering pump thats causing the noise that I know. I did have a pretty bad leak when I first purchased the car but Ive since fixed those and the power steering level is good. Im guessing its the belt or the alternator since everything else has been replaced. I mean the belt looks good but Ive read somewhere they said even though the belt looked fine they replaced it and the noise went away. Hopefully thats the case.

My idler pulley and belt tensioner were squeaky when it was cold and they would become quiet after the car warmed up or on warm days. My indy said once they removed the belts and spun the pulleys, they could hear that they were noisy. Cost to replace both of them at the shop was $410 including parts. The parts themselves were $190.

They are spring loaded, but on each tensioner, one mounting hole is slotted to allow you to adjust the amount of preload. It essentially limits the max tension. Try to increase the tension available.

All pulleys on the main drive belt have been replaced. AC side was actually still pretty good. Only thing I didnt replace were the belts. Im still having morning squeaking but as you stated warms up and its quiet.

Really? Is it on the actual tensioner itself? I have the old one still so i can look on there or are you referring to when you tighten it onto the car you can move the tensioner in one direction or the other???

+1 on the belts. A quick Visual Check will show wear and cracking. Easy replacement.