This article in Fly Fisherman indicates that the river should be open below Banff...
Alberta's Upper Bow River, by Jim McLennan
"Seasons on the Bow
Because so much of the river remains open through the winter, and because the river upstream of the Highway 1 Bridge below Canmore remains open to angling, a surprising amount of fly fishing is available in what is normally considered the off-season. On the right day it is possible to ski at one of Banff's resorts in the morning and fish the upper Bow in the afternoon."
I also says that the river in this area "isn't generous" & I might need a guide to make it worth my while.