I would have a major issue with any horse stuck outside with no shelter in inclement weather like you describe. A blanket is no substitute for getting out of the wind & wet but I realize not everyone has that boarding option.
That would be the only time she really needs a blanket, otherwise I personally wouldn’t put one on her.
She is fat and has a good thick coat and as long as she stays that way she shouldn’t get cold especially if inside. That blanket list idea of your BO’s has too many ways a staff member can get it terribly wrong.
A percentage of barn workers seem to be unable to feed supplements correctly even when pre bagged , so I would be worried about my horse sweltering in a blanket when temps happen to swing or they get the forecast wrong.
I haven’t blanketed in decades but I used to and it was hard enough to get it right even when I did it myself, let alone trust someone else.