Today I noticed that inside the woodchuck fence, the ice had mostly melted, and outside, it had mostly not. Why?

I’m guessing that inside the fence, the beds are covered with leaf mulch, and outside, the earth is covered with dead grass. The dark mulch absorbs heat, but the pale green or straw-colored grass does not. So, after fresh snow, the inside and outside snow pack start out even, but as the melt proceeds, the layer between the earth and the snow begins to show through. When that happens, melting accelerates where heat is absorbed. Confirmation of this idea comes from inside the fence: The icy areas are stone dust paths, which are not mulched, and are light-colored.

The effect shown in the image demonstrates the permaculture principle of stacking functions: Not only does leaf mulch improve the soil by (1) rotting and (2) capturing moisture from the melt, it also (3) raises soil temperature (which should extend the season, if only slightly). Leaf mulch for the win!

Oh, we see, once again, how water instruments the land.