Here, I'll give you an exercise to get used to the cold water.
Get in the shower, you can make it warm to start. Now slowly turn the dial to cold and stay under it. That's what it feels like, but the water temp is actually closer to 70 degrees.
Now if you really want to give it a go, put the water on cold, and take a shower in that from the start. When people in South Florida lost power because of the hurricanes, that's what we had to do. After taking cold shower after cold shower, the water stings. If you talk to people who went thru the hurricanes, a hot shower is one of the things missed the most.
The good news, is that after you swim in the cold water, you can relax in the lazy river which is heated. The showers are also heated with warm water.
Wear 2 t-shirts, and you'll have the wet suit on over that.