Is one obligated to repeat the prayer if it was shortened in congregation due to cold or light winds, knowing that these conditions do not permit shortening the prayer? And what is the ruling on shortening the prayer with the Imam in such circumstances in the future?

Since you have learned that combining prayers is not permissible in those situations, you are not allowed to combine prayers with this Imam in the future, unless there is a valid excuse that permits combining. Indeed, combining two prayers without an excuse or need is not permissible. As for your past prayers: if you combined prayers by delaying the first to the time of the second (Jam' Ta'khir), then the prayer is valid and does not require re-performance. However, if you combined prayers by advancing the second to the time of the first (Jam' Taqdim) in a situation where combining is not permissible, then the second prayer is invalid because it was performed before its prescribed time. Therefore, you must re-perform it. Based on the opinion of Shaykh al-Islam Ibn Taymiyyah, you are not required to re-perform it if you were ignorant of the ruling, but re-performing it is safer in all cases.