I do think it's an important life skill to be able to swim, as well as adding fun to life, especially if you live at the seaside like me. But you don't have to spend a fortune on swimming lessons, just take them swimming frequently. My daughter could swim unaided age 4 having been frequently since babyhood, having a float jacket which I gradually took the floats out of until she could do it without realising. People who sign their kids up for a week's intensive course and expect that to cover it are fooling themselves. If you don't reinforce with plenty of practice they still won't be able to swim and you'll have spent lots of money for nothing.
As regards 'if you fall in a cold river...', yes of course no child will swim as well fully clothed after a shock fall into freezing water as they will in a nice warm pool in their cosi, but the child who can swim in the pool will still fare better than the child who is terrified of water having never been taken to the pool and who can't swim at all.
By the way I totally agree with GrimmaTheNome that there is no point sending them to classes to perfect their technique/teach them butterfly, unless you're actually thinking they may end up being a national swimmer or something. Unless they are keen to do that stuff, just be happy if they are happy and confident in the water and can swim enough to save themselves.
Classes for swimmers which do lifesaving techniques and swimming in pyjamas type activities would be more beneficial than butterfly (yes I have a chip on my shoulder about butterfly having been forced to attempt butterfly unsuccesfully as a child - OK?!) :-)
Happy swimming (skip the classes - just go!)
Vicki