So far, all I've found on the Death of Harald Hadrada from a quick Google search was that he died in the Battle of Stamford Bridge, No shit. The only actual explanation of how he died that I could find was that one page (the Civilization wiki, I know it's not the most reliable of sources but I couldn't find any better) that said he was killed by an arrow to the throat, but that can't be true as Harold Godwinson's army had no archers, at least not in the battle of Hastings.
Any answers would be great appreciated.
thanks.
The source on that is the Saga of Harald Harðráða in Heimskringla, a work written by the Icelander Snorri Sturluson around 1230 or so, in other words at least a cenury and a half. The text says, in part 96:
Haraldr konungr Sigurðarson var lostinn öru í óstinn; þat var hans banasár (King Harald Sigurdsson was hit by an arrow in the throat; this was his mortal wound)
Notably this is in a prose passage written by Snorri. The text is interspersed with poetry which is older and not written by Snorri, and used by him as a source. (and since it's harder to change poetry without screwing up the verse meter; it's generally thought the poetry sections are relatively unchanged). In other words, the information that he was was hit by an arrow in the throat specifically is an oral tradition Snorri's heard but it's not as reliable as other parts of the story.
None of the details in Snorri's text can be regarded as definite truths; on the contrary its clear some details are a bit wrong; e.g. part 86 makes it out that Harald laid siege to York at Stamford, and generally it seems Snorri assumed the location was much closer to York than it actually is.
So Snorri (and/or the tradition he drew upon) could definitely be wrong. An obvious source of such an error would be someone getting their Harolds mixed up and drawing on the arrow-to-the-eye that killed Harold Godwinson.
The simple answer is the the Anglo-Saxons had archers, and used archery in battle. It is very unlikely that Harold Godwinson's army, either at Stamford Bridge or at Hastings, had no archers. The usual Bayeux Tapestry-based story is that the Anglo-Saxons had few archers compared to the Normans, based on only one Anglo-Saxon archer appearing in the Tapestry, compared with many Norman archers. (But also note that it is usually thought that the Normans also used crossbows, and none are shown in the Tapestry, so appearance therein isn't the final word on the presence of weapons at Hastings.)
Thus, it's quite possible for Harald to have been killed by an arrow. Whether or not he was killed by an arrow is another story, as discussed by u/Platypuskeeper
There was recent discussion about Anglo-Saxon archery by u/BRIStoneman and u/Hergrim and myself in https://www.reddit.com/r/AskHistorians/comments/d76tz2/the_origins_of_the_english_longbow_and_archery_in/ which covers some of the evidence for Anglo-Saxon archery and their use of archers in battle.