Sounds as though your heater core is giving up the ghost Ryan. Under the heater core and evaporator coil is a tray that accumulates condensation from the evaporator core to keep your interior dry in the even of a core rupture or during normal usage of the air conditioning. This tray dispells condensation to the ground via the hose you mention. If your core is leaking then this tray accumulates coolant as well and in turn discards it to the ground. The cores sometime rupture on these cars but it is rare. Typically it is the plastic piping manifold and/or O-rings that seal it to the core that fail over time. It is strongly advised however if taking on the tear up to replace the heater core when going in due to the ratio of heater core cost to labor cost, labor being the heavy hit for this job...don't want to do this job twice in the near term.
I have changed mine in my E-32 and is no picnic...about a 3 out of 5 wrench/beer job.
If the first time, document everything you remove and use your digicam.
George