How to Get Snow to Appear Under Trees in Existing Worlds
Why your old trees are still bare
Snow Under Trees only places snow under trees while terrain is being generated. Chunks you already explored were generated before the mod was active, so their trees keep the vanilla look. There is no background process that retroactively sweeps the world.
Making existing areas snowy
1. Identify the snowy biome region you want fixed. Note that the mod keys off biome temperature, so it only affects cold biomes (and cold microclimates like snowy taiga, snowy plains, and similar).
2. Force those chunks to regenerate by deleting them from the world save's region files, or by using a chunk-deletion tool if you have one available. Back up the world first.
3. Revisit the area so the game regenerates the chunks. Snow layers should now appear beneath the leaf canopy.
4. If you do not want to lose builds, an alternative is to manually place snow layers under each tree with a shovel or by letting snowfall accumulate naturally.
Verifying it worked
Walk under a tree in a snowy biome and look at the ground directly beneath the leaves. You should see snow layers where vanilla would have left bare grass or dirt. If the biome is not cold enough, no snow will generate regardless of the mod.