because cold air has more mass then warm air which in turn gives each cylinder more charge on the intake stroke which will drive the pistons down faster on the the power stroke
Cold air intakes are usually placed in the fender well area, which brings in a cooler charged air from beneath the car (outside of the engine bay), which is denser and therefore creates more power.
If it's cold outside do you want cold air blasting when you get in your car?
Have the battery checked.
no
No, it does not loose power but when the engine is cold, it is just harder to turn over.
The air on the inside of the car is warmer than the air outside.
Could be that your low on power steering fluid. When it's cold, the fluid is more viscus, but once it warms up and thins out there isn't enough.
An example is when it is cold outside and your in the car and the windows are frost
If its installed correct and is a good product it will not harm the car, cooler wheater gives your CAI more cooled air = more power.
F1 car has more power and it is lighter than GT1 car
Yes, it does have an effect, but the real problem is the starter trying to turn over a very cold engine. The oil is thick and it takes much more power to turn the cold engine over.
On cold days, your car will not reach a temperature below the outside temp, but instead be on the level or slightly warmer (depending on color of car and interior and how well sealed it is). On a hot day a car can reach above 100F depending on the outside temp and colors and ventilation.