If you look at the actual harmonics of a string and of horn, you will see how wrong you are. There is a reason why they sound different to the ear.

It’s because of this that you can have a relatively inexpensive synthesizer (not sample or PCM based) that does a crude job of mimicking these different instruments by just changing the harmonics.

There is one important difference between the harmonics of string and wind instruments: it's possible to build a wind instrument that suppresses (although not entirely eliminates) the even harmonics, e.g. a stopped organ pipe. If it sounds like a filtered square wave it's definitely a wind instrument. But if it sounds like a filtered sawtooth wave it could be either.