Correct, and moving water (rivers) take it 20x as fast.
The other thing is, due to the gasp reflex and other signs of cold weather shock, you can have real deterioration of your response time, coordination and judgment long before hypothermia sets in.
I've been hypothermic twice, once long ago on the icy Pine River in May, again on Lake Superior in August along Pictured Rocks. Made me more aware of how I react to cold water and to take better precautions in what I wear, eat, drink etc.