Pooh's Corner is AMAZING and can be found at the very end of Critter Country, just beyond Splash Mountain and the Winnie the Pooh ride.
The mint julep bar is behind the French Market, near the train stop in New Orleans Square. It's not ALWAYS open, but I've found that it is more often than not. It's the same building as French Market, it's just a window around back. You'll be able to see it from the dining area of French Market.
Low and behold you are right!! I guess I have been depriving my kids of Mickey beignets for no reason (we don't typically do sit down restaurants in DL).
Pooh's Corner is where Splash Mountain exits. When you get off the ride, you are there! When we ride Splash Mountain, we will ride on Pooh's ride if the line is short, otherwise, we get our treats (Tigger Tail, Chocolate Pretzel, Cookie) at the store!
Also, if you take the train from MS to NOS when you disembark you can see the Mint Julep window at the FM. It's just to the right as you leave the station.