Your history is very consistent with cold-induced hives. This condition involves itchy hives with or without swelling of the skin. The underlying cause is unknown. Typically, young adults are affected. This occurs in 0.05% of individuals and is seen more commonly in colder climates. This condition can resolve in up to 50% of patients.
Symptoms are usually limited to areas exposed to the cold. Less frequently, generalized symptoms such as anaphylaxis can occur. An allergist can perform testing to confirm the diagnosis, but the history is enough in most cases. Avoiding exposure to cold is the best prevention of reactions. This can be difficult at times. High-risk activities include swimming (e.g. cool or cold pools or lakes) and having cold drinks or foods. Antihistamines (e.g. cetirizine) can be used to control symptoms. Epinephrine auto-injectors are prescribed for patients with a history of cold-induced anaphylaxis. This should always be carried.
In summary, your history is very typical for cold urticaria. Consult with an allergist to review your history, and discuss testing and a management plan.