New Hampshire's primary is not closed. People who are not registered with either major party are able to vote in either side's primary, but they are only allowed to vote in one or the other, not both.
In 2008, 54.6% of all New Hampshire primary votes were cast on the Democrat side, to 45.4% for the GOP. It flipped in 2016, with 46.8% of votes being cast on the Democrat side and 53.2% for the GOP.
The primaries are held on the same day so there aren't confounding issues like weather or competing events to muck up the apples-to-apples comparison, and New Hampshire is, electorally, almost exclusively white (see the Sailer Strategy).
Could this be indicative of an impending stronger showing among whites in 2016 for Republicans than in 2008 (and 2012)? Will this potential advantage accrue to any potential Republican nominee, or will it only materialize if Trump gets the nod?
Relatedly, maybe it's a reflection of which side appears to offer the greatest candidate variation. Republicans clobbered Democrats in votes received in 2000, 61.3%-38.7%, but ended up getting just 54% of non-Hispanic white support and narrowly losing the popular vote. McCain won big in New Hampshire that year but Bush ultimately won the Republican nomination.
Was the Republican nomination in 2000 seen as more of a struggle for the heart and soul of the party than the Gore-Bradley contest was? It doesn't seem difficult to make that narrative fit 2008 with Obama and Hillary, when the Democrats got more votes. In this reading, nominating someone other than Trump won't hold much promise for the GOP's chances in November.