Air supported structures forming an enclosure via internal pressurized air, and methods of making same, are disclosed. The structures include an outer membrane defining an outer surface of the structure. The structures include an inner liner blanket coupled to the outer membrane via a plurality of spaced baffles extending from the outer membrane into the enclosure, the inner liner blanket and the inner surface of the outer membrane forming a heating pocket therebetween within the enclosure extending along a first portion of the outer membrane. The structures also include at least one input channel in communication with the heating pocket, and at least one heated air system configured to selectively direct a flow of heated air through the at least one input channel and into the heating pocket to heat the first portion of the outer membrane to remove and/or prevent frozen precipitation accumulation on the outer surface thereof.