Alexei Navalny was arrested on Sunday.
The Russian president removed a sheepskin coat before entering the icy water and submerged himself three times.
The United Nations and Western countries told Moscow before the ruling to let Navalny go.
The prominent critic, who was poisoned last year, could be jailed for 3.5 years.
A massive frozen waterfall has fallen on a group of tourists visiting a Russian volcano.
He accuses Putin of ordering his poisoning with the deadly nerve agent Novichok.
Investigators from the Sverdlovsk region said a child was among those killed.
"We can say that [Navalny] has a pronounced persecution mania".
He was accused of using disproportionate force on the paedophile.