Would more energy be used in winter running the cabin heater or in summer running the a/c
Honestly, I can’t say.
That’s too specific to the cars. Of course, I don’t even know which one you are referring to, ICE or EV? And even for EVs, with or without heat pumps?
At best, I can only give generalizations.
Not to mention, I’m not an expert or anything close to the matter.
For ICE, an A/C compressor is typically connected to the engine through a belt, which is driven by the crankshaft. So it directly uses up some engine power. A few ICE cars use electrical compressors (hybrids, like Prius?). Using the heater doesn’t require any additional effort from ICE, since all you’re doing is venting air that was passed over a heater core (one of the radiators from the engine). Even if you don’t need to heat the cabin, that heat will still be generated. ICE loses MPG in winter for other reasons.
For EVs, in both summer and winter, you need to divert energy to do either. Pre-heat pump, you “only” run the A/C during summer while relying only on a heating element in winter (I think it’s called PTC). With heat pump, the compressor is now used all the time (heating is just the “opposite” of cooling with heat pump). If there isn’t enough heat, a Tesla runs the motors “inefficiently” to generate it. And if that isn’t enough there is supposed to a PTC as the last ditch effort. Not sure about other brands. The PTC is a big, if not the biggest, battery drain.
And this is focusing on the cabin. Some systems, like Tesla‘s heat pump integrates cabin, battery, battery management and motor circulation together. Even pre-heat doesn’t necessarily separate them completely.