What does it mean to "hide things" in one's writings? Several centuries of criticism have unearthed "things" from Shakespeare's plays and poems that were not obvious to older generations. Those "things" are usually called "interpretations" and are often based on new approaches to literature (new literary theories etcetera). Another categories of "things" are allusions and citations from sources that had not been noticed before. I assume that is not what the question describes as "hiding things".
There is another category of "things" in Shakespeare's writing that has usually not been the subject of serious or academic literary criticism. The type of people who is most active in this area are the proponents of conspiracy theories that not William Shakespeare from Stratford but someone else actually wrote the plays attributed to him. There are roughly eighty such alternative candidates, very often from noble families, because, as we all know, only people from noble families can write great literature.
Let me give one example of the type of arguments that these conspiracy theorists use to support their claims. In Act V, scene 1 of Love's Labour's Lost Costard uses the Latin word "Honorificabilitudinitatibus", the longest word in Early Modern English. John Kerrigan (who edited the play for the Penguin Shakespeare) explains,
Considered the longest word in existence (a renaissance equivalent of 'disestablishmentarianism'); it is the dative-ablative plural of a medieval Latin word meaning, in the nominative, 'the state of being honoured'.
What do conspiracy theorists see in this word? They claim it is an anagram of "Hi ludi, F. Baconis nati, tuiti orbi", roughly meaning, "These plays, F. Bacon’s offspring, are preserved for the world", thereby proving beyond all reasonable doubt that Francis Bacon is the author of "Shakespeare's plays". (The anagram argument was put forward by Edwin Durning-Lawrence. Wikipedia adds that the Shakespeare scholar Samuel Schoenbaum pointed out that "the anagram overlooks the fact that Bacon would have written the genitive of his name as Baconi (from Baconus), never Baconis (which assumes his name was Baco)".)
Returning to the issue of capitalisation mentioned in the original question: Early Modern English spelling was not fixed. (See for example the quotes from Robert Greene and Thomas Deloney in some of my recent questions.) Even in the original 1609 edition of the Sonnets, scholars have been able to detect the hand of two typesetters based on variations in preferences in spelling. (See MacDonald P. Jackson: "Punctuation and the Compositors of Shakespeare's Sonnets, 1609", The Library, 1975.) This means that any attempt by Shakespeare to "hide" secret messages through variations in capitalisation would come to nothing due to personal preferences of typesetters. (And Shakespeare's poems were typeset more carefully than his plays.)
There is, of course, the additional irony that seeing "Winters shall**" as a hidden allusion to "William Shakespeare" fails as soon as one notices that "shall" is not capitalised and that the choice of words to read as "hidden message" is therefore arbitrary. Never mind that an allusion on Shakespeare's own name would add nothing to the poem's meaning. In the two annotated editions of Shakespeare's sonnets that I have consulted (one by John Kerrigan for the New Penguin Shakespeare, 1986, one by Colin Burrow for the Oxford Shakespeare, 2002), no mention is made of this type of hidden message.
Colin Burrow also writes in this introduction to The Complete Sonnets and Poems that
there is no reason to assume that the Sonnets are 'about' one relationship, that they are systematically organized on a numerological or biographical principle, or that [sonnets] 1-126 are addressed to one man (...).
P.S.: The sonnet quoted in the question is not sonnet 3 but sonnet 2.