Even if you can stand in the water it might take you too long to get out of it.
My personal experience and information gleaned from personal accounts here and elsewhere suggests that individuals response and resistance to sudden cold water immersion varies quite a bit. Unless you are certain you can be out of the water in 2 minutes or so, I wouldn't risk it.
You can read and read about the effects of cold water immersion but until you experience it you really don't understand it or know how you personally will react.
My personal experience in paddling in sub 35 degree water is the same as what ByronWalter said above. Even with a dry top and a reliable roll I found that sudden upper body immersion was nearly instantly debilitating.
One of the effects of immersion in water of that temperature is very sudden and dramatic vasoconstriction of the blood supply to the extremities. Blood supply slows to a bare trickle. As a result, your arms and legs can become near useless as soon as your muscles consume the oxygen supply they have at hand, which is pretty quickly if you have been exercising.
I lived in Minneapolis for a decade or so. Every winter typically one would read about a drowning or a few drownings that occurred on one of the small local lakes, often very close to shore (within 6 feet). It was not uncommon to hear the victim described as "a good swimmer", and I remember a couple of instances in which a good Samaritan standing on the bank who witnessed someone struggling to get to shore jumped in to try to save them and wound up drowning also.
Canoe / Kayak Anchors
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Touring Kayak Paddles
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