That is actually really clever russ.
There are two ways that fans might control their speeds.
The first is just what you said - a multi-wind motor, where the stator has multiple windings within one assembly. Each winding has successively higher power, and thus depending on which winding you send voltage down, you will get different speeds.
The other way to do it is to use a single-wind motor, where the stator has only two windings (main and auxiliary, both powered at the same time). In this system you control the speed of the fan by using capacitors in line with the voltage feed into the motor.
You can get an understanding of that here:
So, if you were willing to take your fan apart, you could absolutely control either one of these via relays and some logic.
I should note a few things: In the end I ended up putting all of my ceiling fans that don't really need to change speed often on relays and using built in speed controls to set their speed. I just turn them on and off. This works great.
I only mucked about with the speed control in the fans used in my main spaces.
In the end it probably would have been easier to bring another automation protocol in rather than do what I did. But hey - my EE friends are all bemused by my creative misuse of VFDs, so thats worth something :)
Finally, if I was in a more modern space I would talk to Big Ass Fans about their Essence product. While it is expensive, it does have built-in options for 0-10V control.
-Karl P