So it turns out you guys like older Jeeps. That's cool. There used to be an old Jeep out in the woods that was painted some funny blue-and-white colors. When we were kids, we would sit in it and pretend that we were soldiers. Then as we got older, we used to shoot at it whenever we found ammo. When we didn't have any ammo, we'd hang out around it, until one time, a family of raccoons moved in under the hood and Kenny got bit.
Even if the wire has good...
Even if the wire has good insulation, it can still look like this when you strip it to solder. All is not lost. I like to call the slightly tarnished copper "Stage 1" and the green copper "Stage 2." Grab your can of electrical parts cleaner and hose it off.
Anyway, finding out you guys like old Jeeps got me thinking about that blue-and-white one out in the woods and some of the wires that we borrowed from it to get the El Camino going again. Sometimes old wires can be damaged by weather (Editor's note: oxidized), even if the insulation is in great shape. When that happens, soldering to the wire gets really difficult. Solder doesn't like to stick to oxidized wires, although rosin does. And the problem with that is that rosin doesn't make for a great connection.
Let's face it, replacing all the wires in the Jeep to add a set of driving lights or something similar isn't really feasible. It might be something I'd do, but if the Jeep is running and driving, why ruin that? So the key is to try to clean the wire before soldering, and if that fails, try to find another wire. Worst case is to replace just the wire you need to attach to.

I'll be honest, Stage 2 rarely...

I'll be honest, Stage 2 rarely does it for me, so my next step is to spread the wires out, get some fine-grit sand paper (anything finer than 100-grit works fine), and lightly sand the wires until you see shiny copper again.

Then hit it with electrical...

Then hit it with electrical cleaner, or even brake or carburetor cleaner (mainly looking to get the sanding grit out of there), and go ahead and solder away.

If you do end up having to...

If you do end up having to replace the wire, it is always possible to "de-pin" the connector by inserting a small screwdriver or pick into the end of it and wiggle the wire out from the back side. That plastic and metal wasn't cast as one, it was snapped together by a guy just like you.