If you're looking for a little more immersion, take a look at the Rain and Snow FX mod for PlayStation 4 and Xbox One.
Rain and Snow FX allows your character to show frost and wetness when he or she is in the middle of a rain or snow storm. Skin will also appear wet after going for a swim.
When you encounter rain/water, skin will look shiny and there will be a subtle drip. When you encounter snow, skin and armor will ice over. When you walk indoors or the weather clears up your armor and skin will return to normal.
The mod is a solid alternative to Wet and Cold, a mod that's available for Xbox One but isn't available for the PlayStation 4.