I have an old-style wool quarter sheet that I adore. I place it on top of a standard square pad, beneath the monoflap saddle, and do the traditional fold up the lower corners under the saddle flap to give close contact for my leg. I love this quarter sheet because unlike polar fleece, the real wool doesn’t stretch and hang a mile off the horse’s tail. It retains its shape and drapes nicely over the hind quarters, even on windy days (though it has a removable tail cord with snaps). It’s warm, but breathes well too. I try not to get it dirty, not so easy to clean, but honestly I haven’t had to wash it in 10 years. If the horse is likely to sweat, I don’t use it.
True, I cannot remove this kind of quarter sheet without removing the saddle. But I only use it on cold days when hacking and when I wouldn’t want it off anyway. For fast work days, I either don’t use a QS or I use the light fleece cutout style, suffer with it around my legs through warmup and then take it off.