WI the arrow missed King Harold in 1066...

and he did not die on the battlefield that day?

You may get a more organised resistance to the Normans, but ultimately he will be defeated before too long. If he flees to Yorkshire or somewhere, the "Harrying of the North" may be even more severe, though it was bad enough in OTL.

In the (unlikely) event of him going into exile in Scotland (or similar) you could perhaps end up with a more acrimonious relationship between William and the Scots, though I'm not really too knowledgeable on this area.
 
If Harold survives Hastings, he would just summon more men to the English Fyrd, and continue to wear down Duke William and his army, which are largely composed of mercenaries.
 
Could he steady the line at Hastings and allow his forces to hold the high ground rather than chase the Normans back down the hill.
 
Could he steady the line at Hastings and allow his forces to hold the high ground rather than chase the Normans back down the hill.

You have your timeline mixed up. Harold's death is generally thought to have occured during the final Norman assault, when the English shield wall collapsed. Harold surviving may allow the line to hold (although at that point, he has already missed his best opportunity to carry the day), or allow the Anglo-Saxons to retire in something resembling good order, but there is no charge for him to hold back at this point.
 
Agreed with others; Hastings was already unwinnable for the English before Harold's death. If Harold lives he might be able to withdraw his forces in good order and call up more of the Fyrd to rebuild his army, but there was no chance of winning Hastings by that point.

For turning the tide at Hastings, not having Harold's brothers Leofwyne and Gyrthe killed early in the battle might be a better PoD; losing two of his more reliable field commanders made maintaining discipline difficult. Alternately, simply have William killed when his horse is shot out from under him; most of his army thought he was dead for a while.
 
Another alternative way for a Saxon victory would be for Harold to charge with the Huscarls immediatly after the repulse of the initial norman attack. A full-fledged counterattack, instead of the dissorderly mob of fyrd who left the shield wall, could probably have routed the Normans, especially if they can dispatch William.

Agreed that, by the time Harold fell, the English were a lost cause for the day. Harold could possibly retire with the core of his forces intact, and replace a fair portion of the lost fyrd with new levies (if nothing else, recalling those soldiers who had been with him at Stamford Bridge), and offer battle at some later point in the campaign. But the very best that he can hope to achieve at Hastings with this late a POD is a bloody stalemate, and even that probably forces him to withdraw. In all likelyhood, William is going to come away from the battle bloodied, but in control of the south.
 
The POD might have been for the Saxon's to remain behind the shield wall and not counter attack and stick to a defensive position to wear the Normans out. Harold's army was tired from Stamford Bridge and would have had problems defeating the Normans. A defensive position night have worn William's army out. Had Harold escaped he might have formed a rallying point but it is possible the Norsemen would have invaded the north and England would have been two kingdoms
 
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