Bodies of water in Skyrim have different temperatures depending on the surrounding temperature.
This option can be disabled by selecting Lite Mode, or by going to Survival Settings, Gameplay, Frigid Water is Lethal. SkyUI 4.1+ Users: This setting is on the Gameplay page of the MCM.
"Many have saved themselves from a watery death only to die on land minutes later."
Being wet will increase your exposure more quickly than if you were dry. You can become wet by swimming in water, standing in rainy weather, or standing underneath a waterfall.
You will dry off in several hours on your own, or quickly when near a fire. If it's raining, you must be in a tent or underneath shelter to dry off.
If you must travel in the rain, a cloak can help you stay dry considerably longer. Wearing a travel cloak (included in Frostfall) or a cloak from Winter is Coming, Cloaks of Skyrim, or Black Sacrament will keep you dryer, longer. All cloaks provide 10% Exposure Resistance, and allow you to stay dry 50% longer in the rain.
If you're looking for an increased level of depth for your gear choices, including cloaks, check out the W.E.A.R. system.