Hi 3dpotato,
Suggest you research the the reason for the implementation of this by-law. Hopefully an adequate explanation will be in the notice of meeting for the meeting at which it was approved. As raised by Jimmy, there may be physical or engineering constraints.
It specifies split systems only? Ducted systems also have outdoor units, and these days box units jammed in windows are very unfashionable. Again, the “why” for this by-law may be helpful, as simple aesthetics is not consistent with only banning split systems.
One would think that the right to enjoy and use one’s property would include, as well as having a pet, the ability to heat and cool the premises.