Hose at front of air box??? What is it?

What is that cloth like hose with a spring around it that connects to the lower front of the air box? And what does it do?

Mine is disintegrated.

Do I need to replace it?

It helps the car warm up when its cold

Like muddy sez. It's a "pre-heater" for the intake on Renix era Jeeps. You could replace it but it doesn't exist on later models. Mine were both disintegrated, both deleted with no ill effects, AFAIK.

The preheat hose as one of the posters referred to it isn't really to help it warm up, but rather to prevent "carb" icing. In climates where it hovers around freezing and the humidity is high, as the air gets sucked through the throttle body, the temp drops and the humidity in the air condenses and covers everything with a coating of ice. Any pilot is very familiar with this problem. In climates such as here in Colorado, that is a very rare occurance since the humidity is normally quite low, but back east it happens much more often.