Doubt it is the reason in this case but i know that british endurance horses may be trained in winter with full coat plus multiple rugs ahead of getting clipped out and flown to the uae to compete
It would need delicate handling for sure if you thought she wasnt going to take your advice very well, but at the same time, if it was me, id have to say something!
You could always act a little clueless and say something along the lines of 'iv not seen a horse lunged with a rug on before, is it for any specific reason?' See what her explanation is, and then offer the advice of not boiling her horse while its being exercised xD
I have only known one other person to lunge with heavy rugs on with a plastic non breathable bag round its neck and that was my boss who said it was to 'sweat the weight off him'
In my experience saying a word will leave you more frustrated and annoyed. Most of the time these people are not the "just don't know" types, they know everything!
We have one here too and portrays herself as knowing everything. The first authority on horse care. Alas her horse suffers. Her quality of care is best suited to model horses. I've said my piece and it's up to YO to deal with it. If it were my property she would be gone.
I take Ethel for walks in her HW rug but we only go out for about 5mins just walking in hand so she doesn't get hot at all. I wouldn't lunge her in it though, she'd end up sweating buckets the way she sometimes decides to just fly round in trot and completely ignore me Poor horse
I think I'd just make a 'friendly' comment, such as 'Gosh, doesn't he get hot under that rug? Mine would be sweating buckets!' and see if that promotes discussion.