One question and concern I have is do you think with the coop 4 ft away from the 6 foot fence will it still give my chickens sufficient light in winter time?
When you locate your coop and run within your yard, make sure to make room for a 3 ft apron between your coop and the 6ft fence that encloses your yard. Some folks will recommend a 2 ft or 18" apron, and that may work fine, but in my experience, I need a minimum of 3 ft to get a mower between my fence and my coops, and to trim shrubs and trees that try to come into my yard from my neighbors' yard. To me it makes sense to put an apron down over that entire area.
I have had coyotes and cats, racoons, and possums at least, and something has been digging less than 3 inches from the outer edge of my 3 ft apron. If it had been less than 3 ft, the diggers might have gotten in.
For an apron, use 1/2" hardware cloth, and secure to 2"x4" at the bottom of your run using radial washers and screws (into wood), or use staples to secure your apron to the bottom of your run 2x4, and then screw a wood trim piece over top that hides the staples (otherwise racoons can rip out the staples). You can secure the apron to the ground with landscaping stakes of any length that makes sense to you. Grass will grow through and you can mow it without running into the hardware cloth as long as the ground is pretty flat. I've used 12" stakes and 6" stakes in clay/loam soil with about 50% roots, and it works fine for me.
If you make a totally predator proof run (enclose the entire thing in 1/2" hardware cloth, and make sure there's no gaps larger than 1/2" ANYWHERE) and coop, then you can leave your pop door open all the time without worrying about predators or mice/rats getting into your food - this eases the stress of chicken chores significantly. Anything less than 1/2" in diameter (small snakes, small frogs, really small mice, insects, etc), the chickens will eat it, which IMO is a good thing. No ant mounds in my coops - those are a tasty treat.
I don't get snow load here, but lots of rain. If you extend your roof overhangs by 6" to a foot beyond the typical 1-2 inches normally expected, you may cut down the water that makes it into the windows of your coop, or under the roofed surface by a lot. A dry coop is a healthy coop. You can extend the 2x4 that support the roof also, to support the overhangs. Use hardware cloth to cover any open areas under the eves, which I think you were already planning to do.
Good luck!!!