The "indoor" pool... is the thalassotherapy pool. It is covered by a removeable roof... which never is removed. Because the thalassotherapy pool is an integral part of the Spa, it is limited to Adults 18+.
Unfortunately, on Alaska itineraries where the weather could be bad, it would be the only swimming option.
The Millennium class ships, which includes the Infinity have what is called a Therapalossy pool (spelling is terribly wrong!!) which there was a big to-do about at this time last year. I was on the Infinity last August to Alaska, People were complaining in the spring that Celebrity had began to charge a $15 daily fee to use the pool ( it has jet streams and metal rollers you lay on and get massaged by the water but swimming is prohibited and I think the age limit was 18 to keep out children. Well so many people complained because the brochure said it was free. My TA and others received a credit from celebrity, between $50 a person and some said up to $100. Anyway, in the end Celebrity caved in and agreed not to charge. Truth is kids went in, people did swim but it was nice and not usually too crowded especially after 4PM, it was nice to go in for an hour before dinner. It was also great since the Alaskan cruise is usually too cool for the outdoor pool. I am going on the Millie this summer and look forward to it again. I haven't heard that they have decided to charge but it's possible.