I've been there in February before and the indoor pool was opened. But note it isn't really what I would term a "resort" pool. It is a basic, not too large, plain pool. You can probably find pictures of it online if you do a search.

Also, while going in summer, you will almost certainly have better (i.e. hot) weather, there is a downside, traffic and crowds. Come summer, the whole Destin area will be swarmed with thousands of vacationers. Traffic is a whole different beast during the summer months. And yes, SanDestin is a bit east of Destin and has a lot of amenities right there, but if you want to find a nice dinner restaurant, you might find driving west toward Destin (and then returning back to Sandestin) can take significantly longer than it would during the shoulder or winter seasons. But you will find more places open during the summer months (i.e. Big Kahunas, etc.). So it is really a trade-off that you will have to decide which is more important/better for you and your family.