I swim in an outdoor pool which is great in the summers but really crap during the winters. It is Cancun but the water still gets cold enough to be thoroughly uncomfortable. And the wind chill factor is pretty harrowing as well.
So I wear a wet suit in the pool.
There are a couple of tips about wearing a wet suit.
First of all, it's called a "wet suit" for a reason: you're wet inside the suit. There are also "dry suits" (mostly for cave diving and diving in frigid waters) which keep you dry. The difference with wearing one and not is that it keeps you warm. The way a wet suit does that is that the water that gets into your suit and is held close enough to your skin so that it heats quickly. The water inside the suit acts as a buffer and keeps you even more warm inside the suit.
Tip #1: make sure the wet suit fits and is especially flush against your crotch. This is to avoid choking yourself from the pull of the suit around your neck.
Tip 2: if you are planning to do paddle or fin work, bring them to poolside before you hop in. If you get out after swimming for a bit, because of gravity, the water creating a shield of warmth between your body and your suit will rush out and smooth the suit downwards causing it to sit lower on your body. Once that happens, it will be very hard to get back into place and will be very uncomfortable to swim in.
Tip #3: Because it's chlorine, you'll need to soak and rinse the suit thoroughly once you get home. Dry the suit inside out so that the lining dries first.