What is this hose?

Im still prettty new to sleds, so identifying everything is still pretty tough for me.

I need to know what this hose is, and what size it is to replace it. I've got a chunk worn out of the bottom of it from it rubbing on a bolt head, and I THINK it is a coolant hose - AC Part number 0610-076
Im not sure about that. And that is not my engine, so I cant just look at the hose and see what size is on it. Mine doesnt appear to have the size written on it like that one does. Almost looks like 5/16" in the pic.

I also have a coolant leak Im having a lot of trouble finding. Lots of coolant in my belly pan, with no obvious source. This is the only potential source I've been able to find. Can anybody tell me when this hose (assuming it is actually a coolant hose) is pressurized? Anytime it's running? Only when the thermostat is open? Only when running at elevated rpms?

I havent pulled it off yet, but if anybody knows the size I can run pick some up today.

So I went to Advance Auto, and they did not have any 5/16 coolant hose. They said their coolant hose started at a half inch.
They did have 5/16 fuel line, which I went ahead and picked up. Is that ok?