This is a topic that tends to be a touchy one for horse people. Though I really don't understand why some get so heated about it!
Simply put, blanketing is a situational thing with many factors that impact the choice. What works for one horse may not work for another. To understand blanketing, you have to start by understanding a horses coat and body condition.
Horses naturally will have changes to their coat as winter approaches. They'll go through a shed (much smaller than their spring time shed) and begin to grow their winter coat at the end of summer/early fall. That said, not every winter coat is made the same. Some horses grow thick, long, fluffy winter coats that turn them into puffy wooly mammoths ready for some artic tundra. At the same time, other horses grow a winter coat as long and dense as most people's arm hair. Despite that, the coats function in the same way. They raise up (think goosebump style!) to help create an insulating warm bubble for them. Obviously, some winter coats are better at this job. Wind and water can prevent the coat from doing this function though by keeping the fur down, thus making it more likely for the horse to be cold. Another thing that can prevent the hair from doing this is a blanket.
In addition to their fur coat, you have to consider the horses body condition as well. If they have poor body condition (think skinny/slim horses with less fat deposits), they likely will have a harder time keeping warm even if they have a good winter coat unless you up their calorie intake- and even then some are still cold. Horses with a higher body condition (chunky monkeys) tend to do a bit better in the cold simply because they have more fat reserves (ever had a vet suggest letting your horse shiver off a few pounds?). But even those with a higher body condition can still be cold and may need an increase in calories in or a blanket to be comfortable.
Another thing to remember is that blankets prevent them from raising all the hair up on their bodies. This means you have to blanket them heavy enough for the weather. Putting a sheet with no insulation on a horse can actually make a horse colder than leaving them without a blanket depending on the temperature. As it gets colder, horses need either heavier blankets or more layers to keep warm.
So, when do you blanket?
Again, it's a case by case thing that has to be decided by each owner. At the rescue we blanket each horse according to their needs. Moon has an amazing coat and is built like a little tank. He is generally without a blanket and he loves it! Thursday and Xena don't have very generous winter coats and have average body conditions and are blanketed heavier than Moon because otherwise they would be cold. Coco, while she does have a thick coat, gets cold easily and so is blanketed heavier as well with lots of attention to make sure she's not shivering while everyone else is okay. While the temperature ranges for their blanket weights are similar, there are some differences between the preferences of the mares and so we listen to them. Another thing we factor in is that to have them wear less, we would need to feed them a lot more which isn't always financially possible (especially with soaring hay prices). Blanketed horses tend to consume less because they are not burning as much as they would without the blanket.
At the end of the day, it should really be up to the horse if they need blankets so it's the job of the owner to listen to their horse and figure out what makes them most comfortable!