For flight operations conducted under 14 CFR part 91(other than subpart F) in VMC, what conditions constitute "known icing conditions"? Under what circumstances (e.g., altitude difference or no visible moisture), if any, could a VFR flight operation (other than in an aircraft certified for flight into known icing) be legally conducted despite an Area Forecast, AIRMET Zulu, Pirep or other possible indicator of known icing conditions?
The short answer is that it's up to you as PIC to make that determination; the FAA has no clear definition apart from what a "reasonable and prudent" pilot would do.
The FAA issued a legal interpretation on exactly this question in 2009, here's the closest thing to a definition that they give (my emphasis throughout):
"Known icing conditions" involve instead circumstances where a reasonable pilot would expect a substantial likelihood of ice formation on the aircraft based upon all information available to that pilot. While "known icing conditions" are not defined by regulation, the term has been used in legal proceedings involving violations of FAA safety regulations that relate to in- flight icing. The National Transportation Safety Board (NTSB) has held on a number of occasions that known icing conditions exist when a pilot knows or reasonably should know about weather reports in which icing conditions are reported or forecast
They go on to say that the PIC is responsible for determining the likelihood of icing conditions:
Any assessment of known icing conditions is necessarily fact-specific. Permutations on the type, combination, and strength of meteorological elements that signify or negate the presence of known icing conditions are too numerous to describe exhaustively in this letter. Whether a pilot has operated into known icing conditions contrary to any limitation will depend upon the total information available to the pilot, and his or her proper analysis of that information in evaluating the risk of encountering known icing conditions during a particular operation. The pilot should consider factors such as the route of flight, flight altitude, and time of flight when making such an evaluation
Note that even visible moisture and freezing temps aren't automatically considered to be known icing conditions:
The FAA does not necessarily consider the mere presence of clouds (which may only contain ice crystals) or other forms of visible moisture at temperatures at or below freezing to be conducive to the formation of known ice or to constitute known icing conditions.
The specific regulations mentioned in the interpretation are 14 CFR 91.9 (compliance with the operating manual), 91.13 (no careless or reckless operation) and 91.103 (become familiar with all information relevant to the flight). Those regulations would be the basis for any hypothetical enforcement action:
If the composite information indicates to a reasonable and prudent pilot that he or she will be operating the aircraft under conditions that will cause ice to adhere to the aircraft along the proposed route and altitude of flight, then known icing conditions likely exist. If the pilot operates the aircraft in known icing conditions contrary to the requirements of § 91.9(a), the FAA may take enforcement action.
So the bottom line is: you're PIC and it's your decision whether it's safe to fly or not because there are far too many variables for anyone else to decide. But personally I think it would be difficult for any pilot to say that it was "reasonable and prudent" to fly a non-FIKI aircraft in an area where forecasts, AIRMETs or PIREPS indicated icing.