Should I have showered him?

[Dieu]

This is a ridiculous post/question, I know, but please humour this first time dog owner!
Just back from the park with my 6 month Shih Tzu pup, where he fell into the duck pond. I was right beside him but just didn't think it would happen. Anyway, he was pretty much fully submerged until I fished him out by his harness 1 second later.
It is a beautiful and sunny, but cold and frosty morning, here in the Scottish city where I live. On the walk home he dried off a bit in the sun, but I've just towel dried him and he's having a nap in the warmth of our flat. He's pretty clean and dry now, and doesn't seem at all perturbed by the events.
Should I have showered him though, to warm him right through and get rid of any pond residue on his fur? I thought this wouldn't be the right thing to do, as his thick Shih Tzu coat would have got more sodden than it was from his dip in the pond.
Sorry for the daftness of this, but would rather ask than not! Thanks in advance for being nice and helpful as always

My dog swims a lot in everything from the sea to large puddles ( wallows like a hippo!) , the only reason I would wash him when I get home is if he smelt too awful . That said he goes to the groomers very regularly and I have his coat kept really short .

Thanks Flora! Okay cool, I wasn't sure what the done thing was when one's dog has been in pond water. He is lying sleeping beside me now, and does smell a wee bit ... but to be honest, that's nothing new!

The only baths my dogs get are a swim in a pond, sea or river then a good towelling when they get home. I've never actually bathed or showered them and their coats are lovely and shiny.

I agree with Flora, my dog swims and paddles a lot, I only shower for mud, or general smelliness - and since most of his swimming is done in chalk-bottom streams, he usually smells better after a swim! And, as Ender said, I find his coat looks better for being left alone, though I'm not quite as radical as NEVER showering.