Roof steepness is what determines whether or not the snow will fall off the roof, I don't remember the ideal slope unfortunately but I can tell you that unless you install an active system to melt the snow, it will probably undergo sublimation and you won't see much of it at all.
Sublimation is when Ice evaporates directly and people generally see it happening over long cold stretches where new snow doesn't fall yet the depth of the snow slowly decreases.
If I remember correctly the way that earthships countered this problem was by installing
solar water
heaters and a Photovoltaic panel attached to a pump, so that they could circulate a liquid just under the roof skin and have the snow melt into their collection.
Considering the average american consumes about 45 thousand gallons of water a year, by themselves with no added animal or plant included, that would mean your cabin would need either 4.5 thousand square feet of catchment if you used a similar active system, or 9 thousand square feet of catchment if you had to go by rain alone.
Many people can and do survive on much less than that amount of water, and if you want to do your own calculations, just remember that 1 square foot of catchment provides .623 gallons per inch of rainfall.
Also remember, if you're calculating how much water you will need, that we almost always are using much more water than we actually need to, and if you were cautious and aware you could live on a few thousand gallons, bathing only once a week or so. On the other hand, you have to realise that most people make optimistic calculations and fail to keep up with their predictions.