They do not affect LOD generation and xLODGen or DynDOLOD do not change them.
Whatever is the last plugin to modify the material LOD object shaders is responsible for how snow LOD or ash LOD looks.
Below is the list of form IDs of 4 shaders used for object LOD:
- Skyrim.esm  SnowLODMaterial used for objSnow
- Skyrim.esm [0006AE38] SnowLODMaterialHD used for objSnowHD
- Dragonborn.esm  AshLODMaterialMtns1P used for objAsh
- Dragonborn.esm [04024FE0] AshMaterialSolstheimMtns1P used for objAshHD
The objSnow, objSnowHD, objAsh and objAshHD are identifiers used in the object LOD *.BTO meshes to map to the form IDs above.
HD is typically applied to object LOD models which are using full textures, like for example the LOD for the nearest mountains which is using ..\Textures\Landscape\Mountains\MountainSlab02.dds.
Ash LOD shaders are used in the Solstheim worldspace.
The HD shaders make use of the vertex color alpha value. It controls the intensity. A value of 0.0 is low while 1.0 is high. The vanilla game uses ~0.4 for light snow (object LOD meshes ending in *l.NIF) and ~0.5 for heavy snow (object LOD meshes ending in *h.NIF) .
By default higher LOD levels only use the non HD snow shader as HD LOD objects are only used by the first LOD Level 4.
With mesh mask rules and mods it can happen that both non HD and HD shaders are used in the higher LOD levels and on the map. On the map they might have different brightness because of the INI settings or other additional post process effects.
By default the map uses object LOD Level 16, but it is possible to use object LOD Level 32 for the map. See Maps And Map Mods for more.
To force all snow on the map (if it uses object LOD Level 32) to be flagged HD, set AllHDLOD32=1 in ..\DynDOLOD\Edit Scripts\DynDOLOD\DynDOLOD_[GAME MODE].ini. Set AllHDLOD32=-1 to force all snow to be flagged non HD.
In case object LOD Level 16 is used for the map the setting AllHDLOD16 can be added, however, object LOD Level 16 is also used in the game, so forcing the flag will adversely affect what is visible in the game as well.