The hose would connect to the low point drain in the cold side of the water system, but you already knew that. If you have a valve to drain the low point drains, it would connect to that valve and maybe the valve isn't shut all the way or is leaking. It is possible the same drain hose could connect to multiple drains if you have valves, such as maybe also serving as the outlet for the fresh water tank drain.
If you don't have low point drain valves, and just pipes or hoses with caps you have to take out and put back, it's almost certainly the cap not sealing well for some reason--either its loose or cracked or something like that. (That's assuming it's not water dripping down along the outside of the hose; if that's the case, possibly it's just condensation on the pipes, sometimes called sweating, that's happening to drip out there...or possibly a little leak somewhere else in the system.)
If the same hose serves as the fresh water tank drain hose, then maybe your water pump's check valve is leaking slightly, which often is due to a bit of debris or dirt stuck in it.