I'm not extremely familiar with NHS', but my understanding is that they are traditionally turned out with a full mane. In light of that, I'd keep it long as would be appropriate for her breed/type.
Flat or occasionally button braids are definitely the tradition and the norm in the hunter ring, and depending on the judge you may be knocked for a full mane. I showed in hunt seat classes, including Grooming and Showmanship (uber emphasis on correct turnout) with a Morgan mix in a running braid without a problem or any funny comments. I don't do shows of any great scale, but in my local area running braids are pretty well accepted in 4-H and open shows.
Ultimately, it depends on how far you want to go in the hunter world. If you're looking to dabble, I would go with the full mane unless you really love the pulled look. If you're looking to make a mark in the hunter ring, it's best to stay traditional and pull for some neat sewn-in flat braids. NSH hunter classes may make allowances because of the breed turnout standard, but I honestly don't know for sure.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown