We get very little snow here in Memphis, but every few years we do get a lingering snow storm. The snow usually does not get over three inches or so, though (except for winter of 85, when there was almost a foot of accumulated snow).
That's the thing, what tends to matter is not just an *average* winter or snowfall, it's what you *occasionally* get. Unless you just don't mind having your structure flattened. But to me, a) because there are animals in it and b) because it sucks to have to replace broken materials and then rebuild the whole thing, it is usually worth planning for the "reasonably foreseeable unusual occurrance", not just what you might get away with in any given winter.
Also your snow is often *wet* snow, either cuz it fell while fairly warm or cuz it fell then got rained into. So, three inches of snow in Memphis is not quite like three inches of snow high in the Rockies.
While I am not going to disagree with Ridgerunner about 'snow load probably comparable to wind load' I would like to point out that this does NOT mean that just cuz your coop has survived a bunch of hard windstorms it will necessarily be fine for snow too. First, because the direction of loading may be different depending how your coop is built, but mostly because a wire mesh run top does not have much wind load but *can* have quite a solid chunk o' snow load on it.
I would suggest that you probably want whatever rafter- or purlin-type thingies are supporting your roof or run top to be spaced *no further than* 24" o.c. for most materials/designs; 16" would be better for really floppy things like Palruf (pvc plastic roofing). Otherwise, in the absence of specific info about local snow load specs or your coop structure, I am going to punt back to my original formula of "either design it the same as other ones that have stood for many years in your area, or beef it up as much as you can get up the enthusiasm for"
It really does not HURT to have a few extra crossbraces or props or whatever, and it really is the PITS to have something damaged or destroyed and think "oh yeah, I'd *thought* about beefing that up..."
Good luck, have fun,
Pat