I'm a big guy too, and 4" tires are all that fit on my "vintage" fatbike. It wasn't so long ago that 4" was as big as tires got, and 5" tires don't magically prevent trail damage either.
While there is wisdom in getting the biggest tires you can, running at low pressures, and all that, it's important to note that riding bikes in the snow is largely a comedy act, and also a blessing. The technology that allows winter riding is still developing and it's amazing, but the level of success is dependent on many variables. When it works out it really is a blessing, and you can't simply buy success.
The snow depth (not often very deep here), grooming, temperature, sun exposure and other factors conspire to determine what is rideable and fun. I can't think of too many days in the last several years where riding on top of the hardened crust was a thing, but it sure has happened. Most often we get a thin layer of snow and ice, or exposed frozen dirt.
Bottom line, use good judgement, have fun, don't take it too seriously.
Oh, and you could consider running a bigger tire in front if your bike supports it... they don't have to match.