This approach works for the voltage alone, but it might decrease the rated power, or will cause the transformer to overheat in the extreme.
The original primary wire diameter was (hopefully) sized for a higher voltage/lower current combination. When you just simply halve the primary coil and keep the original wire size, you'll increase the current density in the primary.
What will happen in your case depends on the original wire size, the transformer size and actual power needed. The chances are, the original wire was already undersized, but you might still get away with this. It all depends how the transformer rated power relates to the soldering iron power. Hopefully the full power is only needed for a short time when the iron is heated up to the working temperature then less power is enough to keep the temperature up.
I'd keep an eye on the transformer temperature, to make sure it doesn't overheat.
What is usually done for user selectable primary voltage is to have two identical primary windings and connect them in serial for 220V and in parallel for 110V.