my gated community has two swimming pools - "indoor" and outdoor.
the "Indoor" pool is actually covered only by a plastic greenhouse, so it's basically outdoor except i went swimming there two days ago and it was toasty warm while the artificial lake right next to it was FROZEN.
in summer they open windows in that greenhouse to cool it down.
it does have an HVAC but i'm not sure it actually needs it.
granted, target air temperature for a swimming pool is about 90F versus 75F for a residence so cooling a greenhouse to 75F will definitely be more challenging than to 90F ... but heating is not an issue
you only need glass on sides facing where the sun is in winter. in fact it is recommended to NOT have glass on sides facing where the sun is in summer. if you simply position glass correctly and insulate properly you may not need anything else at all.
