Heater core drain hose

The heater core has a drain hose that comes out of the core between the two heater hoses. Mine doesn't have a hose and every once in a while it drips some antifreeze out (very little). Question is, where is this hose supposed to drain to? Hope this isn't to vague..
Thanks

 

the leak indicates hose clamp, hose, or the core is leaking
the hose would direct the fluid to the ground

 

My hose goes out a hole in the firewall right under the battery tray.

 

Thanks,
the metal tubing that comes off of the heater core (where the drain hose hooks up) protrudes through the firewall about an inch. I guess since it is going on the ground anyway, i shouldn't worry about a hose. Does this slight leak pretty much mean the heater core is going out? The heater still works fine...

 

Usually the first sign it's on the way out. If it's a minor leak and you still have heat I wouldn't worry about it too much. Just make sure you check the antifreeze often.

 

The hose was originally about 10 inches long and was directed down and back slightly by the body mount. It had a slash cut end on it, I suppose to help prevent plugging.