The DRAIN hose coming out of the firewall is the A/C condenser drain line. It is a drain hose and is draining condensation from the A/C coils, which is normal with the A/C on. You may also be seeing a drain line for the window cowl area. Now if you are talking about either the inlet or outlet hoses going to the heater, then you more than likely just need to replace them.
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.
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 it's leaking from INSIDE the firewall (away from the engine compartment) you probably have a leaking heater control valve or damaged heater core.
heater core leaking
Its more than likely your heater core.
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.
The sunroof on a Chevy Cavalier can often be repaired by replacing the outer seal. This prevents rain from leaking into the vehicle and causing additional problems.
heater core leaks
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
If you mean engine coolant is getting into the car, the heater core is leaking coolant causing the coolant level to drop and that causes the engine to over heat.
Bad hose or clamp where the heater core is connected would be the most likely problem.