Is it possible for a half Nord (let's say a Nord father and Breton mother) to gain entry in to Sovngarde when he dies?
Initially I thought no, since he's not a "pure" Nord. However, I'd imagine racial mingling over four eras would have "diluted" the Nordic bloodlines from Ysgramor and his settlers.
However, this is a question for people with more knowledge than me!

It doesn't even need to actually be a Nord at all. An Altmer could gain entry if they were worthy.

If they have the heart and mind of a nord, and fights for the glory of Shor, Shor will open his realm to them.

As far as Shor's concerned, the Man-Mer schism is probably ideological rather than racial. They are all just devolved Ehlnofey to him.

Btw Is your concern about racial pureness due to the ingame "racism". if so, several Nords, including in Stormcloak territory (not sure if Starmcloaks themselves do), define a pure Nord as an attitude towards life, not a race.

Even an elf can be born with the heart of a Nord.