Earlier quoted context omitted.
Yeah, I thought ð was voiced in old english, but it's been a very long time since I tried to learn it. I do recall that ð was voiced in the old norse that I was taught in college. It probably doesn't matter too much since you don't have an old englishman to speak to.
Both used to refer to the same sound (the first sound of thing), which mutated into what we have today (as in the), in part due to surrounding sounds (note, for example, that words ending in th are soft/unvoiced). The presence of two different characters has something to do with the integration of Latin and runic alphabets, but the choice of which was used isn't clear to me.
Icelandic employs a 19th century reconstruction of the old norse alphabet noting that "Various old features, like ð, had actually not seen much use in the later centuries" - which corresponds to their merger into one digraph 'th' in English. The article also notes that the letter ð undergoes a devoicing depending on its surroundings.
[0] https://en.m.wikipedia.org/wiki/Icelandic_orthography#Histor...