In the Little House books, Laura talks a lot about corn-based foods that the family ate during their time travelling in a covered wagon, such as corncakes, as well as talking about some of the game Pa hunted that they ate, especially smaller game such as rabbits or prairie hens, since they would have had no way to keep meat from spoiling while travelling.
Families in covered wagons tried to have variety of food, including dried and salted meats, dried beans, cornmeal, and flour. They also had coffee, but that was primarily Pa who was mentioned as drinking it.
If there was an opportunity to pick fruits or berries as they travelled, they likely would have done so if they were certain they were not trespassing on anyone’s land.
Some families travelling in a covered wagon brought cows, pigs, and chickens with them, which provided milk and eggs. However, many times they were sold prior to the journey to make it easier tot ravel without as much livestock, or sold to fund the journey.