I'd say for the run make sure to cover the top with wire, so hawks don't get any of your birds, (we have a terrible hawk problem) and instead of worrying about an animal digging under the run at night, make it so you can close off the coop from the run every night. This way, even if something does get into your run, it can't get to the sleepy birds. If you are worried about day time attacks (I don't have any experience with snakes, so I'm not sure how they attack), or just don't have time to close the birds up every night and let them out every morning, you could make a run with a foot of wire coming out over the ground all around the run, to make it harder for something to dig under. Look up pics of the Eglu coop to see what I mean.
For the coop question: It does make it much easier to clean and less painful for your back if you make the coop walk-in size, but you don't have to. One thing you could do to make it feel like you are actually using the space is put high removable (for cleaning) perches. The birds will perch as high as they can, and will especially like it if you put, say, one perch closer to the ground, another a foot back and a foot or two higher, and so on, to create a stair effect for the birds who aren't as good at flying or don't like to be that high.
About the heating during winter, how cold does it get? Because if the coop is draft-free, the chickens will be fine if it's not crazy cold. If it gets really cold, do consider making the coop a little smaller, that way the body heat of the chickens will be enough to sustain them. I have heard many horror stories of coops burning down from heat lamps, so I would not recommend using one of those, just too dangerous.
Hope I could help. If you have any more questions, ask them! I will try to answer them as well as I can.
Iris
