It could be a pin hole in your freeze plugs. Over time, they can become corroded and can leak antifreeze. I had a 1998 Dodge Ram van and there were six on the bottom of the engine. Pretty easy to replace. You can find a universal set of freeze plugs and adhesice at most auto part stores. If it is leaking under the body, you could have a leaking heater core or under body lines that go to the rear heater.
heater core is leaking.
Because the air conditioner is running.
Water is leaking on passenger side floor board when heat is on
This is a basic trouble shoot, for the Neon in particular is leaking large amounts of oil on the Passenger side of the engine? Check that the camshaft seal is still in place.
look outside where the drain for the ac is and run a coat janger in there to clean it out.
Have you used your air conditioning lately? The most common reason for water to appear to be leaking on the passenger floorboard is that the condensation drain for the air conditioning is plugged. Unfortunately, the drain is pretty much inaccessible to the average person and I have yet to discover a reasonable method of clearing it other than paying the dealer or a mechanic to do it. The other, less common causes for that type of leak is that the heater core is leaking, in which case the fluid will be antifreeze rather than water, or the door seal on the passenger door may be leaking, or the windshield gasket may be leaking.
If the hose is leaking, replace it.
The two most common possibilities are a plugged up condensation drain for your air conditioning, and a leaking heater core. You will usually smell antifreeze from a leaking heater core. Another less common problem is a leaking windshield gasket.
Replace the part that is leaking
It sounds like the heater core is leaking. Check for the smell of antifreeze and that will confirm the bad heater core.
Check AC drain and clear the blockage. Also look for firewall sealer skips.
Replace the part it is leaking from.