I guess it depends a lot on the type of dog and the fur they have but mine dries off in a couple off in about 2 hours, she is a poodle though...ha ha, dogs can smell, just like people.
My common rule is that the dog needs to complete his swimming routine by approximately 3:00 P.M. in the afternoon to get dried off enough for the great sleep at night. The places that I go are considered wildish and there are no restrictions for an animal to go swimming including moose, bear, beaver, deer and those nasty creatures called HUmans.
There's nothing like watching a bare bear go swimming.
You don't want a wet dog in your tent with you