I don't really see anything major happening if it's just sitting there. Least you're not driving it in all the garbage they put down on the roads to get rid of snow and ice.
You may get premature rust or aging. But for only 3 weeks? I wouldn't even worry about it. And NO harm will come to your paint anyways. Ice and snow never hurt nothin'. Clear is VERY tough stuff!
I don't understand why anyone would leave their bike out in the weather. " COVER IT " Too much money out into chrome and such. Too much elbow grease put into cleaning and shinning,.........So my answer is No! don't leave in the snow.
Don't worry about it. Three weeks in the snow won't hurt anything. Three weeks in a lake would be a problem, but anything less is nothing to worry about.
There are many alternatives to leaving your machine to rot. A $20 storage unit.
Two pallets, 4 sheets of plywood, and a few 2x4s will make a jiffy storage shed in your yard, or even an apartment parking stall.
Aint no reason to leave it out in the weather
i'd at least cover it and get the wheels up off the ground, would give me a little more peace of mind, a lot of things that are covered and concealed on your car are exposed on your bike.
but like others have already said, after 3 weeks you're not going to come outside to a rust bucket, not even close.