I know that hydrochloric acid reacts with a heated mixture of iron and sulfur,
"... a heated mixture ." is a student's way of saying "a mixture of iron and sulfur that has been heated." That is, HCl reacts with pyrite, marcasite, troilite, and however many other iron sulfides. The key point here is that the "heated mixture" is not iron, nor sulfur, and does not exhibit the chemical properties of either of the elements from which it was prepared.
but why does it not react with an unheated mixture of iron and sulfur? (During a demonstration, I could see a soggy mixture of the powder and fillings in the acid, and I noticed nothing so I am assuming no reaction occurred. Is this correct?)
You did not see any vigorous evolution of gas, therefore, no rapid reaction of acid with metal (it is proceding, but slowly at room temperature), nor did you see any other obvious signs of other chemical reactions that are occurring in the "soggy mixture." The point of the demonstration is that the compound, iron sulfide (I'm not going to hazard a guess which) has different properties and reactivities toward HCl than do the constituent elements.