IOTL Harald Hardrada's sons Magnus (whom he'd left behind as regent in Norway) and Olaf (who'd been with Harald in England, and survived) had already become recognised as kings -- with a north/south partition of the country -- by the Norwegians by summer 1067. ITTL maybe Olaf didn't get back home after all, especially as an easier English victory over the Norwegians -- leaving more of Harold's housecarles fit to fight against the Normans too -- could have been a key part of the POD (Maybe the big Norse warrior who held Harold's army at bay on a bridge for a while IOTL while other Norse got their armour on simply wasn't there ITTL?) but in that case Magnus would have been sole ruler and thus in an even stronger position ...Well, I think Harold would spend the winter and spring getting ready for a foray into Norway with his spiffy new navy. If he doesn't do it the Danes will, and I don't think he'd want the Danes that powerful.
This means that the English would have been attacking an established king (or two), rather than a people cast into disunity by their King's death overseas, which would probably have been more difficult... and I strongly suspect that, after having had to deal with two invasions (and a number of raids) in one year, relatively few of the English would have felt like volunteering for an overseas campaign anyway. The 'Fyrd' couldn't legally be required to serve overseas, right?
Furthermore, the way in which fiords and mountains divide Norway mean that anybody trying to conquer it in this period can't move troops around between the regions very easily overland, and in winter trying to move them by sea would have been rather risky too. Therefore the choice for a conqueror would be between planting garrisons in each separate area, thus risking defeat in detail, and leaving some areas ungarrisoned even though those would probably become centres of rebellion, and the Norwegians weren't exactly known for liking the idea of foreign rule: Look at how short a reign Canute's [half-English] son Swein had had there, for example...
Personaly, I think that leaving Norway for King Sweyn of Denmark to get embroiled in -- which would have kept him too busy to consider invading England -- would probably have been a wiser idea.