Some of the best flyfishing fiction is written by Keith McCafferty who is an occasional visitor to this board. His Sean Stranahan novels are set in Montana and are truly a good read. I think he has done seven of them to this point.
I've seen threads like this before on other sites and, unfortunately, what are usually recommended are books of essays with perhaps a few short stories (which are fiction.) Tom McGuane, John Gierach, David Ames, and many others are great authors, but for the most part it's not fiction, let alone novels. Mc Guane did do 92 in the Shade which is saltwater flyfishing fiction, but his other novels are not FF related to my recall.
Most of the FF novels, or novels by what are usually regarded as flyfishing writers, are "whodunnits." Most are quite good. William Tapply has a whole series of novels that are in addition to his fine collections of essays. John Galligan has done a few, including The Blood Knot. If you're interested in fishing, but it doesn't have to be flyfishing, Crunch and Des is terrific, although more accurately referred to as a collection of short stories all based on the same characters. It does read very much like a novel, though.
Enjoy your winter of reading!