In Haptic Shared Control (HSC), human-like reference generators and adaptive strategies have shown promising potential for minimizing human-machine conflicts, though these advances have thus far been limited to simple control tasks. This paper extends the application of low-conflict HSC to a more realistic driving task. An Adaptive HSC (A-HSC) design for constant-velocity steering under changing visibility is proposed, where the A-HSC dynamically adjusts its steering support to align with the human driver's behaviour. In a human-in-the-loop simulator experiment with 16 subjects, the proposed A-HSC adapted successfully to the drivers' steering behaviour, converging to an average look-ahead time of 0.46s in low visibility and 1.01s in high visibility. When visibility decreased during the task, the driver's trust and control authority influenced the adaptation, with half the drivers complying with the A-HSC support allowing it to retain high-visibility settings. The A-HSC outperformed the fixed low-visibility HSC system in reducing driver control effort, minimizing conflicts and improving subjective acceptance. However, it ranked lower than the fixed high-visibility HSC overall. To further enhance A-HSC adaptability and driver acceptance, future research should investigate how varying the authority balance between the HSC and the driver affects adaptation, and explore more intuitive HSC structures, potentially based on the driver's visual aim point.