Scenario: Object 1, a bridge freezes over do to the surface area exposed to the below freezing air. Object 2 has the same surface area exposed to the same air, but its base sits on the ground that is above freezing. Would object 2, with the same amount of surface area exposed to the same air freeze or would it pull heat from the ground through conduction to not freeze? If object one had more contact with the ground to draw heat, would that prevent a bridge from freezing?
The surface in contact with the earth enjoys the benefit of conductive heating. Being cooler, the energy of the warmer earth will be transferred to the earth-bridge, ostensibly until the energy imbalance is removed.
The air-bridge is going to become colder due to the colder air and will also continue to get colder until the imbalance is removed. Huge masses of the planet earth can require extensive time to remove such an imbalance. Poor conductivity means a slower transfer but local weather conditions such as sunshine and seasons are considerations.
The temperature difference between the earth and the air is a factor. If the cold air is chilling the earth-bridge at a rate higher than the earth is warming it, the air wins.
It might require active or passive energy transmission devices (heat pipes) to provide enough energy to the air-bridge to prevent freezing. Geothermal energy is based on this concept, loosely speaking.
There is much more complex physics involved in this type of question. Your question was phrased at a layman's level, hence my layman's answer. I didn't do well enough in physics class to provide formulae.