Swimming in cold weather can jump start your system, so to speak, but overall it's a mental configuration of getting acclimated to the temperature of the water.
Why? Because it's there and who seriously doesn't like a challenge? Even despite the cold weather, some may just slap on a pair of swim trunks and take the plunge for the heck of it. Aside from the apparent "Hey, I did it!" appeal of winter swimming, there are actually many religious connections involved. In Eastern Europe, many do it as a way of celebrating the baptism of Jesus, while others claim that it's a way of purifying the soul, which may be why many jump into freezing water on New Year's Day as way to start from scratch.
Ice cold water can be a jolt to your system at first. However, if you haven't swam for a while, or aren't in the best shape, it can have serious effects. If you're not adjusted to the temperature, you can start to get cold and have issues with losing your body heat; your muscles can actually slow down causing weakness in your limbs.
This is one reason why you may want to limit the amount of time you actually spend in cold water. Hypothermia can occur when your body temperature drops below 95 degrees, which can lead to additional heart issues as well as respiratory failure.
You can also run the risk of shock, hypothermia, cramping and even heart attacks, if you're not prepared. If you do happen to have heart issues, then you should avoid swimming in cold water entirely…the shock of the cold water alone could actually kill you.
If you're not sure that this is for you, then you should consult a doctor to make sure you're in the best shape for winter swimming. But before you turn yourself into an ice cube, be sure that you have the appropriate equipment for cold water swimming. In this case you want to get yourself a full body wetsuit, that will help keep you warm.
Most wetsuits are made out of neoprene and you'll find overall that most wetsuits will have small bubbles that help insulate between the water and your body. Small traces of water may seep seep through the wetsuit at first, but the water will eventually adjust to your body temperature.
You also don't want to get your head wet, so it's not a bad idea to invest in a neoprene diving hood which comes in a variety of thicknesses ranging from 3-7mm. You could also wear a diving cap underneath the hod, to help keep water out of your ears, with the main goal of keeping your head warm. Also neoprene dive booties and gloves will be a great benefit in cold water swimming, with no adverse reactions to whatever strokes you plan on using.