Several Reasons
1. It's old -- Have an auto parts store check it for you. They usually don't charge for such things.
2. It's loose - Same as above
3. The squeak could be coming from the water pump rather than the fan belt- If it's neither #1 or #2 try to find a friendly auto mechanic who will listen to the squeak and suggest a cause and repair.
A fan belt may squeak or slip badly in cold weather due to it being stiff from the weather. However, most likely you will need the belt replaced.
Old fan belt. Try replacing it.
Assuming the belt and pulleys are in good shape, put a dab of clear silicone grease on both sides of the belt. Do this with the engine off. Squeak is gone.
Check your power steering fluid or your fan belt could be making noise.
The belt tensioner may be at fault. Also a few drops of antifreeze on the belt will cause it to squeak and crackle. The pulleys should be cleaned before installing a new belt.
If the squeak changes with fan speed, the fan needs replaced.
I would first look at the fan belt or belts. This is the most common cause but you could have other problems including worn idler pulleys.
It will squeak
you need to get some belt dressing and spray it on the belt it will stop the belt from sqeaking and can be used for all belts you can by it at any auto parts store it is called Belt Dressing it is in an arisal can it works very well.
the shop could have got a little oil on the belt or the pullies it only takes a smug, also if the weather has changed the dampness in the air will act the same way
Belt is most likely loose and/or needs replacing
Belt worn out, or loose.