Since 2011, I have paddled a lot in the winter cold of New England.
I particularly enjoyed the extremes.... Ice paddling, snow storms etc.
My trips would all be in saltwater bays, estuaries, rivers where I could protect myself by planning trips based on wind and tide.
I brought lots of things with me like backup wetsuit gloves because if I fell in, my ski gloves would get wet (they were much warmer than wetsuit gloves)
I always had 1 or 2 cameras
Snacks
My trips were slow rolls through estuaries and creeks... almost never in the middle paddling fast and worrying about cadence and speed.
I typically paddled around 10k... and was out about 2-3 hours
Ok... on to the main question
I NEVER felt any need to hydrate in short trips like that. Ever.
If I brought something to drink with luch, it was totally stupid like a bottle of Diet Coke that I stuck in a pocket of my paddle pants, that I always wore over my wetsuit to carry camera, keys and snacks
Those winter paddle sessions are the thing I miss most now that I am in Florida every winter... down here I paddle shorter trips in any desolate area I can find.... and never bring anything except cameras