Mystery hose?

I was replacing a headlight bulb today when I noticed this hose. It looks like it is going towards the bottom of the radiator but the top isn't connected to anything. The radiator was replaced a few months ago. Kinda hard to see in the picture but the top end is right next to the battery. I could not find anywhere this would go.

Hard to see whats what, maybe a protective covering for one of the hoses or lines.

Hard to see whats what, maybe a protective covering for one of the hoses or lines.

I was thinking it could be a cover for the line it's next to, but not sure.