This show could go either way. Since there's no information on it I'll give a very broad opinion. I have faith in Netflix to understand there is a way to appeal to adults with animation without alienating the kid audience, and vice versa. That balance is crucial to the show working at all, especially with a description like "Family-friendly Game of Thrones". The balance has been found and used well before in Batman: The Animated Series and its sequel shows. I'm not saying Bruce Timm must be involved, but they would be doing themselves a favor by hiring any of the older DC Animated Universe writing staff they can get their hands on.
Many comments I've read have said Link should or shouldn't be mute, and I don't care too much about that. My favorite Zelda game was on Nintendo 64 and he definitely had a voice there but didn't speak (and didn't need to). Based purely on the Game of Thrones comment, I'm going to assume he will be a Jon Snow type character, important but not necessarily the lead, and as such, he will likely have to speak. Just don't make him annoying and I'm sure it'll be fine.
That said, the Game of Thrones comment worries me because if you boil it down, it's just another soap opera with family drama, and the Zelda universe doesn't have many named families/clans/houses unless you count the different species. There's "regular?" people, forest people, rock people, water people, and desert people. And there's monsters. Assuming the show isn't based on any one game, I'm worried that the plotlines will be soap opera-ish.
Anyway, there is little to nothing concrete about this show so far so this is all pure speculation.