The effect of increasing the pressure difference and decreasing the area cancel out, and the buoyancy is the same if the hot dog were horizontal. Vertical hotdog has big pressure difference but small aera. Realizing that the buoyancy comes from both the height and the surface area of the ends, one might guess correctly that the buoyancy depends on the volume of the object. Buoyancy also depends on the density of the fluid. Fluid can be defined as a liquid or gas.
Water has enough density that the buoyancy on a hot dog in water is enough to make it float.
Of course, in the atmosphere, the air density is much less - about 0.001 times the density of water, so a hot dog would not be buoyant enough to float in the atmosphere. The Greek mathematician and engineer, Archimedes , described the amount of buoyancy force on an object as equal to the weight of the fluid that it displaces. The weight of the fluid displaced is this displaced volume times the fluid density. Since the buoyancy force on an object in the atmosphere is so small, an object must be very large and very light to get enough buoyant lift to be useful. Hot air balloons use the buoyancy force for lift.