"I have been submerged in water with ice on it (when the air temperature was 20) and while I don't like it, there was no gasp reflex (I suppose I should check to see what that is"
Yes you should check into the gasp reflex because that is what kills most people in cold water. It's a reflex when instantly immersed in very cold water. A lot of experiments have been done and it's pretty unusual not to have any gasp reflex without pre-conditioning even at much higher temperatures than water near the freezing point.
I would be willing to bet if I capsized you in your boat in your skirt in 33 F water you would have one hell of a panicked gasp reflex. It does not matter if the water is 3 Ft deep you can still drown if you aspirate a little bit. At the very least buy a wetsuit and a hood. And if you don't believe the people posting here. Go do a test with someone nearby to help.
Hardshell Kayak Sail Rigs
Touring Kayak Paddles
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