Any chance the song is "Wild Geese" by Ian Tyson? It's definitely Canadian, but doesn't mention a river by name, but it's a pretty song any how, so here it is.

WILD GEESE by Ian Tyson

Wild geese flying by, calling on the downwind as they go
No answers they send, and springtime has too many miles to flow
The lone black pine, hillsides all covered with snow.
Why does the wind say you ain't coming back any more?

Was there a time when my dreams were not always of you?
The days ain't so bad, but each night takes so long passing throug
Down by the stream, fresh otter tracks in the snow
Why does the wind say you ain't coming back any more?

I've got a mind just to ramble this whole country round
With the fields turning green and the frost boiling out from the ground
Drive through the miles of country I've never seen before
Now that the wind says you ain't coming back any more.

Repeat v. 1 if desired

Recorded on the Ian & Sylvia Vangard album "So Much For Dreaming" which has been reissued on CD

rich r