Are you sure it's because she's broody? I've had a few leghorn hybrids and none of them have ever gone broody, especially in November. Is she eating and drinking, moving around OK, or does she appear lethargic when moved out of the nestbox? Nostrils and eyes clean and clear? Any breathing noises? Is she moulting? (You say she's young, does this mean this is her first winter, when moulting is unlikely?)
If she seems normal apart from the need to sit in the nestbox, could you perhaps make a small enclosure within the run where she will be in the dry with food and water but no access to a cosy box, then observe how she behaves? Normally, a broody hen removed from the nestbox and penned outside in the light will walk around all the time making a big fuss. If she just cuddles down in a corner there may be something else wrong with her. Access to light is essential because this will affect hormonal balance and help restore a broody to her senses, whereas staying all day in a dark box will intensify the broodiness, if that's what it is. After roosting time, go down and put her on the perch with the others overnight so she doesn't get cold out on her own. This would be the usual way to break a broody hen and should work within a few days, but also it will guide you by her behaviour to know if anything else is going on.