Where does snow falling at the polar ice caps originate?

When snow falls at the polar and Greenland ice caps, where did the water originally evaporate from?

I can think of two ideas:

1. The water mostly evaporated from the nearest ice-free ocean because water vapor that evaporated further away falls as rain before it is transported to the poles
2. The water vapor mostly evaporates in warm oceans nearer the equator, and is transported by wind / jet streams high in the atmosphere

Which of these two ideas is more correct?

More precisely, what proportion of snow falling at the ice caps originated from different latitudes? This might include water that evaporated from last year's snow fall

How do we know, and are there some good studies to look at?

Thank you