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If you wear breathable bib style (not talking PVC crap) waders with a wading belt or two, with a dry jacket and a PDF is going to keep you pretty dry even if you go for a swim on a cold day.
Even with a splash jacket you aren't going to fill up with water and drown. You get enough water into know you got wet but changing your undershirts is usually enough to get back out and paddling again.
I wouldn't wear waders without at least a splash jacket, PFD and belt but the for mellow conditions in the early spring it will keep you pretty dry and warm for a lot less money then a dry suit.
Couple of videos on waders if you take a swim: