Nobody makes a fender that will work with a 4" wide tire. But there are some ingenious folks who have hacked together some pretty fine solutions and put them out there on the interwebs for all to see. I'm going to attempt to pirate one that I particularly dig.
Fatbikes currently use 26" wheels/tires, but by the time they get all pumped up and fat, their OD is much closer to a "normal" 29er tire. So my starting point is a brand new set of Planet Bike Cascadia 29er fenders. I shudder when I think about how I will be harming then.
The deal is basically this: You split a very nice, shiny set of production 2-1/2" wide fenders down the middle, and hack in a center section to make them 4+ inches wide. It sounds simple enough, but I'm fairly sure that I'm gonna have about 300 hours into a set of fenders that ends up looking like a kindergarten art project. Unfortunately, I'm all jacked up to give this a go and could care less about the value of my time.
Removal of all the hardware and mudflaps is the first thing that needs to happen . . .
Leaving you with a sad, non-returnable pile of parts that looks like this . . .
Once everything is stripped off the actual fenders, you're free to buzz em through the saw. I started with the front fender and it was a little rough. I refined my technique and the back fender came out a lot cleaner but trust me, of these two extremely boring videos, you want the shorter one . . .
The end result then, of the first hundred hours, is four pieces of plastic.
From the ashes of this dumpster fire something fabulous will eventually rise. Possibly.