It won't matter which Nook model one owns, just as long as the owner has a valid and paid NYT subscription. However, just like with the Kindle, Nook owners won't be able to take advantage of this feature immediately. No time frame has been given except that an e-mail will be sent in the "coming weeks" with more information about free access to the NYT website.
I don't use an e-book reader to subscribe to the NYT, and I can imagine it would be frustrating not to just have this all be available at once. I do use the Nook Color to subscribe to a few magazines, but none of those have websites that are blocked by a pay wall. However, none of them have as much content (especially not as much original content) available online.