To me, and this is only my opinion, I don't think its "right" for the Dragonborn to be anything but human. Also, just because your character is a Nord that doesn't mean they were born in Skyrim.
I would go with Nord because it makes the most sense for being Dragonborn and you are in Skyrim and no they don't get treated as outsiders but all other races do.
In Morrowind the Dunmer seemed to fit the story better. In OB it was an Imperial. In Skyrim a Nord.
Course you can play anything, but I just feel more attached to the MQ if I use what I feel is the 'canon' race. Most my characters don't do the MQ so it's rarely a problem anymore.
Another quest that to me has a canon race is the Civil War. Nord for Empire or Stormcloak. Imperial for Empire. Other races just wouldn't seem to care IMO, unless I made a very specific role-play for it.
Then just skip the dialogue and "RP" that you already know it. As many times as I've played through this game, I ignore most of the dialogue options anyways. But as far as the whole "not being born in Skyrim thing" that's the only way I can come up with a satisfactory explanation of why our character is treated the way they are by the different NPC's in game, and why we're caught crossing the border into Skyrim at the start.
edit - @ LeBurns to me, Oblivion was the only game that didn't have a "canon" race to the MQ. But, as far as Skyrim and Morrowind are concerned I agree with you 100%. And, as far as the CW goes, I think any race can join the Legion but only Nords should do the Stormcloak side. There's no way I could see a Dunmer going for a stroll in Windhelm and thinking to themselves' "yea, this Ulfric guy is who I should be fighting for." It would be kind of like a Jewish person fighting for the Nazi's in WWII.
Orcs in the Legion are commonplace. It makes sense for an Orc character to join them.
Wasn't Mankar Camoran a Dragonborn though? He was an altmer, but he could wear the Amulet of Kings and shout, according to his commentaries. I think that's proof enough that even non-human races can have a soul of a dragon.
It can be anything you want really, but if you're strictly fulfilling the Nord prophecy than be a Nord. If you're more open-minded though and realize that the Nordic prophecy is probably just a version of the same prophecy that is told several different ways through different cultures under a different name, be anything you really want to be.
My true Dragonborn characters are Mer (Altmer and Bosmer), and they make perfect sense too because of the rise of the Dominion (and hopefully in the future, the eradication of the current incarnation of the Thalmor).
Empire. A lot of Orcs are in their Legions anyway, and they're treated well there.
I say go Nord for your DB. It just feels right.
And a very easy-to-spot sign of said Nord not being raised in Skyrim.
Nords are good, but you could also have an Imperial, I believe Nords and Imperials had a common ancestor millenia ago
Argonians make the most sense to be Dragon Born..
They look like Dragons