Just had to remove an ice water line to a 1/2 bath wall hung lavatory.
There was a hot water on the left. A cold water on the wall above the sink right in the center, and an ice water on the right.
The sink and faucet were Kohler, and the faucet manifold had a port for the extra cold water feed which was clearly from the factory.
I've never seen an ice water to a bathroom sink before.