The only hose connections at the firewall that contain coolant are the connections at the heater core. You either have a loose clamp or the compression fitting between the steel and metal parts of the hose itself are leaking. If there is coolant leaking out of an drain at the bottom area of the firewall, there's a good chance that it's leaking from the heater core itself, through a drain pipe which is the same drain pipe that removes water condensation from the air conditioning.
If it's leaking from INSIDE the firewall (away from the engine compartment) you probably have a leaking heater control valve or damaged heater core.
The coolant sounds like it is leaking from the drain hole for the heater core. The drain is usually along the firewall and keeps the coolant from entering the vehicle should the heater core develop a leak.
Your engine may have a leaking hose connection or a leaking gasket at the water outlet. It could also be a leaking hose.
heater core leaking
Its more than likely your heater core.
Most likely it's a ruptured heater core, leaking coolant. But before you replace the heater core, check the connections outside the firewall. Sometimes a leaky connection will drip to the inside... but don't expect it; it doesn't happen often.
You probably have a bad heater core. The heater core is installed in a plastic casing and the spout is there in case it starts leaking. This keeps it from leaking into the floor of the car.
If its inside the cab at the firewall, its probably your heater core which is located on the passenger side under the dash. This repair is usually not much fun. If its leaking in the engine compartment near the firewall, its probably a heater hose that is failing. This is an easy repair
heater core has a leak replace heater core
Bad hose or clamp where the heater core is connected would be the most likely problem.
Leak in heater core.
If coolant is leaking from the back of the engine it is most likely that the intake gaskets need replacement or a possible heater hose connection depending on the year.