So important british people in 1066.
North Wales was ruled by two allied kings, Bleddyn ap Cynfyn in Gwynedd and his brother Rhiwallon ap Cynfyn in Powys. They'd been placed on those thrones by Harold Godwinson in return for agreeing to be vassals and allies of Edward the Confessor.
They apparently took this vow seriously enough that after William's conquest they joined up with the saxon rebels and helped the fight against William.
However Harald has an in here which William did not. His son Magnus had fought in Wales in 1062, possibly alongside the ap Cynfyn brothers and definitely alongside the man who's throne they usurped. Gruffydd ap Llywelyn who's two sons (Maredudd and Idwal) would later try and regain their father's kingdom and attack the ap Cynfyns.
Again Magnus should know all these people and might be able to make a deal with one of them on behalf of his father.
South Wales seems much weaker. The only king of note there is Caradog ap Gruffydd who tried but failed to unite all of south wales. Wales was undercut massively by constant fighting between the petty kingdoms while also facing invasion from Norman England in otl, you'd imagine the same would be true here. One of the kings, Maredudd, seems to have even gone over to the normans willingly in return for land in England so there's no reason he wouldn't also make a deal with Harald.
In terms of Saxon Rebels, the main noble opposition (not just random rebels like Eadric the wild or Herewood the wake) came from mercia and Northumbria, where another pair of bothers, Edwin and Morcar were in charge. They were the first people Harald fought and beat in his invasion so they'd probably be just as opposed to a Norwegian England as a Norman one. If he leaves them in power they'd be trouble. But he has less reason to do so than William as Tostig and Copsi, who were on Haralds side, had previously run Northumbria. Northumbria was the heart of the rebellion against William but it might actually be more comfortable with a norse king given how many danes lived there.
Then there's Edgar the Aethling, who was chosen as the new saxon king while in his early teens in 1066 and surrendered without a fight. He would probably also rebel if left alive as he did against William.
He in otl had the support of the second most powerful king in the british isles, Malcolm III of Scotland. Now Malcolm was a constant thorn in William's side (recognizing norman overlordship one day and then raiding Northumbria the next) but he was married to Harald's niece and had harboured Tostig prior to Tostig's alliance with Harald so he might be less hostile vs Harald (or he might be more so as harald will have him surrounded in a way William did not).
All of which underlines the main advantage Harald has which William did not. Harald was already an established part of british politics. He had prior relationships with the danes (it's much harder to see Sweyn attacking Harald in England the way he did William) and the scots and the irish and the welsh. Which means he's likely to have less hostile relationships with the other british kingdoms than William did.
I actually think for a bunch of reasons (Normandy was more rebellious than Norway, there had been norse kings of England before, etc.) Harald is going to find ruling England easier politically than William did.
The question is militarily. The Norman's were much better castle builders and cavalry men than the Norwegians. Even if they face less opposition they still might be less successful than the normans.