David J. Peterson, conlang creator for HBO's television series Game of Thrones, had this to say:
Also, the information on Skroth there [Wikia] is wrong. I created something for the White Walkers initially called Skroth, and I believe they didn’t end up using it. And that was for season 1; I didn’t do anything for it for season 2.
— David J. Peterson, "Ei Mahrazhi’th Drivoe", Dothraki.com
In other words: they developed a language but it was never used, and there is nothing in the show displaying White Walkers communicating with language in any way other than potentially telepathically, even to each other, let alone to the wights (members of the army of the dead), while in the books they speak in a language that sounds like ice cracking.
The only instances we've seen in the show that are technically communication (but not really a perceivable language) are the shrieks/screams that both the wights and White Walkers have made.
In "Valar Morghulis" (Game of Thrones, S02E10), the White Walker that leads the army of the dead (and Sam stumbles upon) screams/shrieks with his weapon raised, which seems to communicate to the wights "Attack", or "Onward", or is perhaps a rallying call so that the scattered wights nearby group up and follow him - it's not really known. Out-of-universe, it's a dramatic introduction to the reveal of this enormous army we (the audience) weren't aware of.
In "Beyond the Wall" (Game of Thrones, S07E06), as the group is capturing a wight ...
... it lets out a loud shriek/scream, and this ultimately results in nearby wights being alerted, causing the group mortal peril.
This would also technically classify as communication, but not necessarily a language.
Beyond these rare instances of communication, the wights seem to follow quite complex instructions that indicate a telepathic/magical command from the White Walkers, rather than an explicitly verbal language (like Skroth, or the ice-cracking language of The Others in the books).