In summer the Canoes are open 7 days a week. They seem to open around 10:00 or 11:00 am, and they close at 5:00 pm. They are always open 7 days a week during summer and busy holiday periods like Christmas/New Years, Thanksgiving week and Easter Vacation. During the rest of the year they operate on weekends only.
It's a great way to see the Rivers of America, but be advised that they are real canoes, not on a track, and they only go if you paddle. The guys who run the Canoes will keep prodding those who stop paddling to keep paddling. If you want to see the scenery along the riverbank, it's probably best you sail on the Mark Twain or Sailing Ship Columbia, where you can just stand there and watch it all go by. But on the Canoes, you are down on the water level and you'll be fairly busy paddling and won't have a lot of time to gawk at animatronic moose or Indians.
They still run the Canoes at Tokyo Disneyland too, but I guess they've closed them at WDW and in Paris. Hong Kong Disneyland never had them to begin with. The Canoes are a lot of fun, but I also highly recommend the Sailing Ship Columbia for a "only in Disneyland" experience. The ship is gorgeous, they fire the cannon during the trip, the below-decks museum is very cool, and they currently have a pirate guy on board who hijacks the boat from the CM sailors and tries to get you to do pirate stuff.