I think it depends entirely on your definition of “quirky” behavior and the lengths you have to go to manage it.
My mare hates being cold and will lock up and refuse to go forward any time it’s colder than -10C. I managed that by moving to a facility with a heated indoor arena, which we both enjoy (and so does my coach!).
She also says that leaving her earstuffs in is vastly preferable if you want to hose off her face. She’s learned they prevent water going in her ears. That one is an easy fix – leave them in till after bath time.
She thinks that Canada Geese shouldn’t eat the windfall apples and will try to herd them away from the tree. But she will also gently “escort” them out of the ring to make it safer for the spookier horses. She once did the same with a small mouse wandering in the track of the indoor. shrugs
Other than that, she is the most solid citizen you could ask for and a good performer. Anyone can handle her. She ground ties. You can clip her without a halter. She will do the lead line one day and win A/O o/f the next.
Her son, now 3 years old, is the same. His “quirks” are so far limited to being a pocket pony with everyone he meets (he has zero stranger-danger instincts) and a fascination with zippers. He just likes the noise of a zipper going up and down. As quirks go, I think I can live with that.