I did not find any "William Horn" serving in the Light Brigade during the Crimean war, however I did find records pertaining to "William Horne" in the 11th Hussars (this may be a misspelling on the original documents, which was a common problem).
The information I have on him, from my book,is as follows:
Horne, Pte William, (831), 11th H Born in York [57-1-24]. Enlisted 11-06-34 [57-1-24]. Prior Occupation: Laborer [57-1-24]. At Newbridge 1st& 2ndMusters [54-1-5]. With the Depot troops 2ndMstr [54-2-5]. Invalided 01-01-57 at Chatham [57-1-24]. DNE (did not embark for the Crimea). Not on MRs (medal rolls).