My Corolla screeches when I start the engine during winters. I thought the starter,alternator or battery was bad but it only happens at low temperatures. If I warm the engine, shut it off and then start again even in winter no screech. It doesn't screech during summer.
What could be the problem?

Sounds like you need a new Serpentine belt...for a TEMP fix, you can try rubbing a lil STP oil on the belt "inner side" where the groves are...

Your belt is slipping.

It just sounds like your belt is old and need replacing.

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Don't apply STP oil or any oil. The oil will make it slip more. You may NOT hear it because it is lubricated. But it will slip MORE and eventually your belt will fail sooner.

Adding oil could cause your belt to NOT drive the accessory (like AC, alternator, etc.) causing you to think other failure ($$$).

Good Luck...

It's normal. Oil sticks the engine parts together, use synthetic and low viscosities. Re: that serpentine belt, keep it fresh, due to frozen alternator and water pump. Got a block heater to plug in? That noise and wear is super hard on the engine!

That happened to me several times when i was in the military and it was the belt sticking to the pulley. As you found out like it did after you started your car up no problem.