Why is the plural of reindeer sometimes "reindeer"?

Why is the plural of reindeer sometimes "reindeer"?

Wiktionary has the following etymology:

From Middle English, from Old Norse hreindýri ‎(“reindeer”), from hreinn + dýr ‎(“animal”).

while the etymology of deer doesn't have any mention of Old Norse, so I assume knowing about the pluralisation of "deer" (from Why is the plural of “deer” the same as the singular?) isn't sufficient to explain this.

Solution 1:

My Chambers English dictionary plainly states that 'deer' is derived from Old English 'deor' and the plural is 'deer'. The plural of reindeer is also reindeer. I don't think this is related at all to the other usages quoted such as: 'there are lion in these parts', 'there are tiger in these forests', 'man first discovered fire when lightning struck a fallen branch of oak'.