We know that in order for third-years and up to be allowed to visit the village of Hogsmeade, they must present a form duly signed by their parent or guardian.
When Harry’s guardians, the Dursleys, miss their opportunity (!) to sign his, he is not allowed to go to Hogsmeade. Both Cornelius Fudge (as Minister for Magic) and Professor McGonagall (as head of Gryffindor House) refuse to sign the form on his guardians’ behalf—probably at least in part because they think there’s a mad killer on the loose looking for Harry, but also, as McGonagall specifically states, simply because:
“You heard what I said. No form, no visiting the village. That’s the rule. […] The form clearly states that the parent or guardian must give permission.”
Prisoner of Azkaban, Bloomsbury/UK paperback, p. 113
Obviously, Tom Riddle did not have any parents or guardians ready to sign his form for him: his mother was dead, his father likely did not even wish to know of his existence, and if he did have a legal guardian at all (I don’t know how orphanages worked in Britain in the 1930s), it was likely to be Mrs. Cole (warning: Wikia link) as the matron of Wool’s Orphanage where Riddle grew up. As Mrs. Cole was perfectly Muggle in every way and was never told by Dumbledore—nor, we must assume, by the boy himself—that Riddle was a wizard attending a wizardry school, it seems unlikely in the extreme that she ever signed Riddle’s form to visit Hogsmeade.1
I don’t recall any incidents in the books where Voldemort speaks specifically of him visiting Hogsmeade as a school boy (then again, why would he?); but being content to remain at the castle while his classmates have fun in the village seems quite out of character for him, too.
Are there any (canonical) indications whether special provisions were made for orphans with no legal guardians to sign, so that they were allowed to visit Hogsmeade after all? Or, oppositely, whether such cases were played strictly by the book and unguardianed orphans, and thereby Riddle, were not allowed to visit Hogsmeade?
1 One might of course easily envision that Riddle simply Confounded Mrs. Cole to sign the form; but that would lead to detection of underage magic (assuming this was even a thing in 1940). Riddle may of course have forged Mrs. Cole’s signature, but that would be rather likely to be discovered as a forgery, since at least Dumbledore was aware that Mrs. Cole did not know of Riddle’s magical abilities.