With growing emphasis on environmental protection and sustainability in highway construction, the high mixing and compaction temperatures of styrene-butadiene-styrene (SBS)-modified asphalt have raised concerns regarding energy consumption and pollutant emissions. Sasobit, a warm-mix additive with a melting point of 99 °C, effectively reduces asphalt viscosity and construction temperatures while enhancing high-temperature performance; however, it may adversely affect low-temperature crack resistance. To address this challenge, this study developed low-dosage Sasobit–SBS composite asphalt incorporating aromatic oil and crumb rubber to reduce production temperatures while maintaining performance. Evaluations on binder properties and mixture performance showed that Sasobit effectively lowers mixing temperatures and preserves rutting resistance, while external modifiers, especially crumb rubber, significantly enhance low-temperature crack resistance (by 24%) and fatigue life (by 50%). Moreover, the crumb rubber formulation reduced production costs by 11% compared to conventional SBS asphalt, demonstrating a practical and cost-effective strategy for improving durability in cold regions.