Chronic Venous Insufficiency (CVI): The patient's history of hormone replacement therapy (HRT), which can increase the risk of blood clots and venous insufficiency, along with the description of a macular pink rash on the medial lower legs, suggests CVI. The absence of pruritus and the presence of hairless, cold legs also support this diagnosis.

Peripheral Arterial Disease (PAD): The difficulty in palpating tibial pulses, reduced pedal pulses, and prolonged capillary refill time are indicative of impaired arterial circulation, suggesting PAD. The patient's use of high-intensity statins, which are often prescribed for patients with cardiovascular risk factors, further supports this possibility.
Lipodermatosclerosis: This condition, characterized by skin induration and pigmentation changes, often occurs in the setting of chronic venous insufficiency. The patient's rash and the location on the medial lower legs could be consistent with lipodermatosclerosis.

Acute Limb Ischemia: Although the patient does not report leg claudication, the presence of cool legs, diminished pulses, and prolonged capillary refill could indicate a more severe arterial obstruction. Acute limb ischemia is a medical emergency that requires prompt intervention.
Deep Vein Thrombosis (DVT): The history of HRT increases the risk of DVT. While the patient does not exhibit typical symptoms of DVT like swelling or edema, the absence of these symptoms does not rule out the diagnosis, especially in the context of other risk factors.

Erythema Ab Igne: This condition, caused by prolonged exposure to heat (e.g., heating pads), can result in a reticular rash. Although less likely, it could be considered if the patient has a history of using heat sources for comfort.
Necrobiosis Lipoidica: A rare condition characterized by necrotic lesions in the skin, often associated with diabetes. The description provided does not strongly suggest this diagnosis, but it remains a possibility in the differential diagnosis of leg rashes.