I've read that Icelandic and Old Norse have a middle voice, so I wanted to know if either or both of these distinct grammatical features existed in Old English.
As far as I can tell from what Mitchell & Robinson say in A Guide to Old English, no.
Verb forms in OE only have one voice - the active voice. The one exception is the word hātte (is called, was called).
If someone wanted to indicate the passive voice in OE, using any other verb besides hātte, they'd either
- use man (one, one person, someone, anyone) alongside the verb in the active voice, or
- they'd use 'to be' or 'to become' alongside a past participle.
I suppose that just because Mitchell & Robinson don't mention a 'middle voice' doesn't mean that OE writers never indicated things which would take a middle voice in a language that has a form for it. Perhaps someone else can comment more knowledgeably on that.