am I alone on this?

According to Dictionary.com, this is the word origin for reindeer:

Reindeer is actually redundant. The root rein is Scandinavian for 'reindeer', so reindeer translates to 'reindeer deer'. It came to English from Old Norse hreindyri.

Did anyone else think reindeer were referred to as such because they were deer with reins attached to them to pull sleighs?