Step,I know exactly what your talking about.I had the very same problem with that hose on my 96 3.8.The thing split like a sliced up sausage.
First,this hose your talking about is the main heater hose.You'll want to replace the rubber hose section only.You can't get "just that rubber piece" at Ford.They sell the whole line only (from the firewall to the water pump,and it's over $80).Instead buy just a small amount of rubber heater hose at any auto parts store.AVOID the brand called "Thermoid" that Advanced Auto parts sells.That stuff has got to be the cheapest ass hose I ever had.I replaced that same hose 5 TIMES before I bought Goodyear hose at Autozone.The Thermoid stuff is soft and VERY weak.It kept bursting everytime my motor hit around 4000 RPM

.No problems with the Goodyear.I believe it's either 5/8" or 3/4" .Not positive.
You'll have to work at it pretty good to get that rubber piece off the metal pipe.I believe the factory had a small pinch clamp on there.Cut or carefully pry the clamp off.To get the rubber hose off,what I ended up doing was use a utility knife and slice a straight cut where it fits over the metal.Try not to dent or bend the metal pipe or else you can't re-use it. Using 400 grit sandpaper or emery cloth ,clean the corrosion off both metal pipe ends (the other one being at the temp sensor plug).Then just use a couple of hose clamps and tighten it down.
Make sure you bleed the air out of the cooling system.Might want to just flush it while your at it.
Don't bother with the nut on the exhaust header.You wont need to remove that unless your actually pulling the metal pipe off.Taking that nut off wont cause an exhaust leak.It only holds the pipe bracket on.The header nut is behind the bracket nut.
Check your radiator for leaks and the coolant condition.It turns out my radiator had too much muck built up inside that it was causing excessively high pressure in the cooling system.It explains the split hose and also the exploded radiator 2 months later
If your coil pack is shorting out when it gets wet,you may want to add some dielectric grease to the inside of the plug wire boots.Unless your coil pack has a crack in it.