If the hot dog is held horizontally, then there is not very much difference in altitude from the bottom to the top side of the hot dog. But, there is a lot of area along the whole length of the hot dog on which the pressure acts. Horizontal hot dog has small pressure difference but large area. If the hot dog is stood up vertically, then the difference in height between the top end and the bottom end is greater, but the amount of area at the end is less. 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.