The misuse of reign for rein is quite common, perhaps because of the decreasing uses of rein in everyday life. Even CNN are guilty, erring in the title of a piece about oil: OPEC keeps tight reign on taps. There are over 8000 hits found for "tight reign" on Google, all of which are wrong.
The easy way to remember which to use in a particular situation is to know that reign, meaning the period during which a monarch rules, is derived from reg, or rex, meaning king. So, seeing the 'g' in reign should remind you of regal. Hence, the other rein must be the horse one.