Okay, am here at the moment and spending a long fasting evening on internet (traveller's tummy anf pregnancy not great combo for peace of mind)z Atlas (along beach from Medina) and Sofitel Mogador have heated pools. They are 200dh (~£16) 250dh respectively and seem to charge same for children. Hotel des Iles has coldest pool ever: 50dh children, 75dh adults. Ocean Vagabond: we were told free if you dine there. We dined but still paid 120dh adult, 60dh child. Tbh failure to find a heated pool at reasonable price has been a bit of a drag but beach is amazing. Very friendly place and minimal hassle. Very relaxed place, doesn't feel like has changed too much in a decade!
The following hotels in Essaouira have pools: Atlas, Hotel des Iles, Ibis, Ryad Mogador, Villa Quieta, Riad Zahra. All are outside the medina walls. All charge something like 80-120 dirhams entry per day, I am not sure if they heat them in winter.
I recently went to the pool at L'Aquarelle, which is a gorgeous country guest house just outside Essaouira (get there in a big shared taxi). The owners were talking about closing over the winter, but as it's inland it's much warmer and less windy than Essaouira itself. Try them: www.aquarelle-essaouira.com (pool was 70dh per person/day, eg £5).
More info and photos of L'Aquarelle on my website/Facebook page: www.maroc-o-phile.com (I am British and have just moved to Essaouira). Mail me via the site if you have other queries.