When I was messing around with the warden again, I found out that it cannot spawn on one snow layer unlike other mobs that can spawn on one snow layer and only one snow layer, not two.

To repeat this, setblock a sculk shrieker with the can summon value,

/setblock ~ ~ ~ minecraft:sculk_shrieker[can_summon=true]

then block every spawnable spot, or go high in the air, and only allow it to spawn on snow layers. You also must have a big enough spawning space as the warden doesn't spawn on a single block from testing.

You can then do this with other mobs like zombies and skeletons and see that they will spawn there as long as it is only a single snow layer and not two or three.

You can remove the snow layer and see that the warden spawns normally afterward.