Horatio receives Hamlet's letter in Act 4.6.12-31. Hamlet trusts Horatio, unlike the turncoats Rosencratz and Gildenstern.
Horatio is a faithful friend. Hamlet calls him "a man that Fortune's buffers and reward hath ta'en with equal thanks...not passion's slave". In other words, Horatio is constant, fatihful in both good times and bad. Hamlet also describes Horatio as "more an antique Roman than a Dane." This means that he is "old school" and tough as nails.