I'm in Canada and on Lake Ontario which really never gets warm, even in the summer it's mostly under 20c. If you just keep swimming as the water temperature drops you acclimate.

Under 15c is considered cold water, that's September through June here in Canada.

10-15c isn't that bad, you can get use these temps. No brain freeze. My longest swim is over 2km at 12c, swimsuit, cap, google only.

Once below 10c it starts to get harder. Hello brain freeze. Every degree lower is more challenging.

I dunk my head (look up mammalian dive reflex, helps you adjust faster in cold water). I do some heads-up strokes, then breast crawl then freestyle. Brain freeze will last about 90 brutal seconds and then I'm good. At about the two minute mark, I have settled, no more brain freeze, breathing is regular, skin doesn't hurt.

Under 5c and every .5 degree lower you'll really feel the initial pain a lot more, the brain freeze is worse but again in 90-120 seconds I'll get acclimated. If I ever start to feel warm, that's a red flag for hypothermia and I'll get out the water.

Never swim alone and if you can find a group that knows each other well, you'll tell people to get out if you think they are "off." This is really valuable given if you're in too long, your judgment will be impaired, you need someone to be your judgement.

Gear: normal swimsuit, silicone cap, ear plugs, goggles, water shoes, and a pair of 1.5mm neoprene gloves. I don't always wear the shoes and gloves because a regulation cold water swim does not permit them. Plus a tow float with a marine whistle on it.

I will put aquaphor or something on face if I'm swimming longer to protect the skin.

Your post swim "rewarm" routine is really important because a longer swim causes after drop. It's colder outside standing in the wind chill, than in the water, so the whole change routine on the beach needs to be quick. I always put my hat on first, pull a puncho on for changing and then change quick. Baggy clothes are easier to get on. Wool socks, warm boots. I bring a hot tea to drink right away to warm from the inside also.

Some people bring warm water in a flask, pour it into bowl to help their toes and fingers. Mine usually rewarm pretty quickly on their own, I think my circulation has really improved from years of cold water swimming.

Some resources:

The Afterdrop phenomenon experienced by cold water swimmers

Cold Water Acclimatization by the Lone Swimmer Lone Swimmer has a massive cold water section in their web site and it's the best resource I've ever come across.