Imagine I made a puzzle, with some hints.
Imagine then that this puzzle of mine is impossible to solve without looking at the hints.
A person who wants to challenge himself by trying to solve the puzzle without any hints, the puzzle would be impossible to solve for that person.
Are these kinds of puzzles allowed?
A hint is not part of a puzzle - it is additional information provided to give people the option of making the puzzle easier. Note the word "option" - it's not a requirement. Putting necessary information in the hints is making the puzzle impossible for those who choose to attempt a puzzle without them. Unsolvable puzzles aren't puzzles at all. They're guessing games.
(This also happens to be current site policy.)
I'm not going to comment on "allowed", but all the information required to solve a puzzle (perhaps assuming vast intelligence and knowledge) should be in the question itself. Hints are for making the puzzle easier, not for making it possible. Allowed or not, a puzzle where this isn't so is almost certainly a bad puzzle.
(Maybe there are weird cases where the point is that crucial information is hidden in unexpected places. Something labelled "Hint" might be such a place. I generally don't like that sort of puzzle, but to each his own. Anyway, most puzzles are not like that.)
