It's not my imagination. I wonder if anyone else has noticed this. It gets significantly lower mileage with heat on during winter, as you probably have also experienced. It actually always gets better mileage with a/c on in eco around 72-74 degrees setting, driver isolation on, outside vent closed. Better than when I just run in fall/spring with no heat or cooling on at all. Anyone else find this to be true?
Other factors can hurt mileage too - colder air is denser causing more drag. Rainy weather and road conditions can have an effect. Your tire pressure can drop a few PSI without tripping the tpms light. The gas engine may run a little longer to get up to temperature than it would in summer and run more often to maintain it. And switching to winter tires will kill mpg for sure.
It potentially can - maybe - or maybe not. But it's something which is very difficult to definitively test. I've tried it - and couldn't notice any difference at all. I recall a test 40/50 years with a chap driving 100 miles with A/C on, then 100 miles with it OFF. And said there was a measurable difference. Until someone pointed out that they were at different times of the day - from memory, the "OFF" was in the hotter part of the day - which could well have affected his mood, and quite a few other factors.
I think what you're experiencing is simply you get the best MPG in warmer temps regardless of A/C on or off. In other words, the A/C, being electric, doesn't really affect MPG regardless of ECO setting. What really affects MPG is running the ICE to provide cabin heat.
Also the winter gas mix has perhaps 3-5% less energy/gal., cold tires are stiffer. After a cold start It takes our 2019 standard Prius somewhat longer to reach its best mileage than in summer, this is a significant factor for trips under 30-40 min. and I sometimes think about whether it would be worth adding a block or dipstick heater on a timer for cold mornings. While it may seem like a significant mpg change, the absolute fuel consumption difference isn't that great.
Your first sentence is true. Your second sentence is false. Your third sentence is true at times when the engine wouldn't otherwise be running. Cabin heat is free heat when it's heat that would otherwise be wasted via the radiator.