There's nothing that says it can't influence the look at least a little bit. Morgiah has her mother's (Barenziah) red eyes but her father's (Symmachus) light skin.
But...Barenziah and Symmachus were both Dunmer. Of course a child takes physical traits from both parents if they're of the same race.
I also doubt the Gray Prince's mother had gray skin.
His father was an Imperial vampire. You'll notice he bears no semblance to an Imperial whatsoever. His gray skin was the result of the vampirism his father had. Vampires aren't a different race, so it's more a case of inheriting a disease.
Actually, you can't even mix and match racial traits/powers in game to cover half-bloods. Appearance is the ONLY way to indicate mixed parentage in the creator.
It would be practically unnoticeable anyway. Appearance does not indicate mixed parentage, according to lore, so no, not even that is a way to do so while remaining lore-friendly.
I consider in-game examples as having precedence over the PR director when it comes to lore canon, but you are welcome to disagree.
And the in-game examples back-up the lore that there are no visible ways to recognize someone with mixed parents. You can give a Dunmer darker skin and what you want to call Redguard-like facial structure or whatever, but that's because Dunmer can have dark skin and different facial structures. It's only when you say he/she looks that way because of his/her Dunmer father that it breaks lore.
Again, everyone has the right to do this as they please, plenty of people mod in races that are clearly meant to represent half-breeds, but the fact remains that doing so breaks the established lore. If you really want a half-breed, then by all means, ignore that piece of lore and have fun.