I have the Newmarket quarter sheet too and I LOVE it! I wanted one with the girth area cut out because my guy likes to pretend I'm not using my leg if there's a 1/4" of fleece between my leg and his side ;)
Also, as the owner of a horse who is super sensitive to static and will leap in the air if he feels the slightest shock, this quarter sheet is the best fleece one I have ever used.
I use my quarter sheet if it is below 40*F or if the wind is making it super cold. It often doesn't last the whole ride as he starts to warm up. I also don't jump with it but I have friends who do and it doesn't seem to cause them any trouble.
I use a Rambo Newmarket quarter sheet on the mare for the first 15 minutes or so, if it's below freezing. Mostly walking, a little trot. She's not clipped, but she doesn't grow much of a coat and has arthritis in her hind end.
That said, I had her out for a walk hack in the snow today in 25 degree temps plus high winds. I didn't use the quarter sheet because I was afraid of her spooking if the wind lifted it. And she was 100% fine without it.
i just bought one off of a girl at my barn and used it for the first time today when the high was 45. I plan to use it when I think it's too cold to ride, since I think it's so cute and it'll encourage me to suck it up and brave the cold. mine'a an under-the-saddle type. I wish I woulda snagged her riding blanket before she sold it as I was still right chilly. My horse did really well with it and it didn't shift on her during our flatwork and she wasn't hot under it afterwards.
RFI-Get thee some dryer sheets and rub the boy's rump with them. Also, put the 1/4 sheet in the dryer with a few. Matty gets electric under his and heigh-ho, makes for a RIDE. I always keep his cooler on his hind end when warming up for flatwork and he doesn't mind a bit (pure wool). His Tack of the Day Newmarket fleece quarter sheet puts him over the moon. His old wool one is fine. If you go fleece, get some Bounce and rub away.
Edited to add, I don't start wearing 1/4 sheets till the temp is AT LEAST 20 degrees or lower...;-/
My TB mare doesn't grow a very heavy coat and this time of year I always put a 1/4 sheet on. The one I have is meant to go under the saddle and then I fold it up so it isn't interferring with the girth and my leg. I have never had a problem with it slipping.