That's one side of the coin. The other: frigid brine on an overcast winter morning, a chilled
snowmelt river in the shoulder season, or just the prospect of a long paddle upwind after an unexpected dunking.
Chilly water--even as warm as 60 degrees Fahrenheit--can be very dangerous: Cold shock and hypothermia are among the foremost threats for any kayaker. The American Canoe Association recommends wearing protective insulating gear if the temperature of the water you're paddling is 60 degrees or colder, or if the water and air temperature combined add up to less than 120 degrees. Your body loses heat more rapidly when it's wet and when it's exposed to a breeze, so getting soaked and then paddling on a windy day can be a recipe for trouble even if the water's not all that icy.
What constitutes protective insulating gear? For cold-water paddling, you want to reach for a wetsuit or a drysuit. The former, made out of varying thicknesses of neoprene, permits a small amount of water inside where it's warmed by your body heat. A drysuit, by contrast, is waterproof: Made from polyurethane or more breathable Gore-Tex, it keeps you dry even when submerged. You should wear moisture-wicking layers--polypropylene is a prime material for this--beneath a drysuit, although you often only need one or two (so beware of overdressing); you don't wear anything underneath a wetsuit.
Consider a drysuit if you're kayaking in particularly cold water or in rough conditions and inclement weather; in such cases, wetsuits often come up short. That said, you can combine a wetsuit with other protective layers such as dry tops, which keep water out of your neck opening and cuffs and seal into your spray skirt.
Neoprene or nylon gloves or mittens keep your hands warm, but you lose some of your touch with the paddle; a substitute is the pogie, a waterproof and insulated pocket inside which you can grip the shaft as usual. Other good protective clothing includes hats, booties, and paddling jackets.
Remember, too, that your personal flotation device--which should be worn regardless of the water temperature--gives you added security in cold water: It provides supplementary insulation, sure, but by doing its primary job--keeping you buoyant--it exposes that much less of your body to the shock-inducing water.