Your symptoms suggest airway hyperresponsiveness or cough-variant asthma, which are highly sensitive to environmental triggers. Since your current combination of montelukast and fexofenadine has not provided relief, the next step is often an inhaled corticosteroid (such as budesonide or fluticasone), sometimes combined with a long-acting bronchodilator. These medications target airway inflammation directly. If post-nasal drip is contributing, a steroid nasal spray may also help. I highly recommend consulting a pulmonologist for a spirometry (lung function) test. This will help confirm the diagnosis so they can prescribe the most appropriate inhaler therapy for you. Meanwhile, wearing a mask or scarf in cold air can help reduce triggers.