There are two wedding veils. One is clearly there in PChat under Standard > Hair > Bridal Veil (second to last choice).
Database entry:
6,"V_Fem_HAIR.GEO/GEO_Hair_V_Wedding_Veil_01","!X_Wedding_Hair_01","!SF_Hair_Wedding_Bun_01_Mask","None",2039583,14935011,1,10203903,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,"capes/CapeWeddingVeil01.fx",2039583,14935011,"Head","standard"
Not all options are available for all costume designs, and sometimes when you make choices, options will become unavailable until you restart the whole creator. For instance, making Choice A will cause Option B to become unavailable. Even if you undo Choice A, Option B will still be unavailable until you restart the whole process. The first thing that comes to mind is that another choice is interfering with the availability of Bridal Veil.
In Icon, a slightly different wedding veil is under Back Details > DevOnly > Cape > Wedding Vail [sic]
The database entry (for those that can parse Icon costume saves) is:
17,"GEO_CapeHarness_Wedding_Veil_01","!Cape_Wedding_Veil_01","!Cape_Wedding_Veil_01_Mask","None",-16777004,-16777004,1,-6573313,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,"capes/CapeWeddingVeil01.fx",-16777004,-16777004,"Capes","DevOnly"
part,geom,tex1,tex2,displayname,color1,color2,color3,color4...fx,color,color,region,bodyset
Testing it, you can also add "capes/CapeWeddingVeil01.fx" to the fx field of any costumepart (the veil will be the colours of that part).