Short answer: At the end of the day all you're doing is melting wax onto a bit of plastic then spreading it around. It's not rocket science, anything fairly hot will work.
Long answer: Most normal irons use a very coarse thermostat to control the temperature. If you graphed the temperature of the base it would look a bit like this /\/\/\/\ with the hottest point being realistically far hotter than you want for waxing skis - it's above the smoke point of the wax a lot of the time, and it is hot enough to damage the base and epoxies in your skis if you're not quick with it.
A proper waxing iron uses more complex temperature control, to maintain a lower, even temperature.
The other issue is that a normal iron has holes in the bottom, which will wick up the wax so it doesn't spread as nicely. A waxing iron usually has a solid base that is either smooth or lightly grooved to carry the wax better.
All that said, I know loads of people who've done their waxing for years with a $2 iron from a thrift shop. It's just somewhat easier with a dedicated waxing iron.