I'm having a hard time deciding if these get apostrophes.
- The beauty of winters first snow.
- The days final light.
If either or both need the apostrophe, where should I place it, and why?
The possessive apostrophe is required in both cases; the snow and the light belong to “winter” and “day” respectively. The apostrophe goes before the -s.
- The beauty of winter's first snow.
- The day's final light.
If days were meant to be plural, the possessive apostrophe should come after the -s, however, I would also recommend adding an adjective, or any qualifier, before the noun just to clarify.
- The autumn days' final light.
- The final light of autumn's days. (paraphrased)