The real question is whether you use pins and clips or whether you're the kind of boater to put 303 on your boat and clean out the PRV each time you take your boat out. If you clean your PRV each time, put the cooler in the back. Unless you drain it often, then put it in the front but it should be turned around with the hinges facing the rower, but only if you've got a drybox too. Only on alternate weeks, however. If you use pins and clips but don't 303 your boat each time you go out, the cooler should go in the back with the hinges so it opens from the back. Honestly, there's a really good rationale for all this but I can't remember exactly why now. If you want to know, you'll have to search for a thread that went through the whole thing back during the drought of 2003 when we had time to analyze this kind of stuff with decision flow charts and everything. The flow charts were really cool.
Whatever you do, remember if you don't get it right the first time, you'll have to move the cooler to the other end of the boat the next time you go out.
Good luck with this critical decision. Don't screw it up.
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse