Wolverine had been in the river for a full day before he was dredged up by Striker. He can regenerate, but how does he come back from the dead?
The movies have not really examined the extent of Wolverine's ability to regenerate. In the comics they have been dramatically extended over the years to the point where he can survive being near the centre of a nuclear explosion.
Specifically on the issue of drowning, the story arc "Drowning Logan" (Wolverine (vol. 5) #5 (Jun. 2013). Marvel Comics.) specifically covers what happens when he is trapped underwater for an extended period. This damages his long term health, but does not kill him.