Summer, from December to March, is the most comfortable season: longer days, warmer weather, and the best chance of dry windows for walking. It is also the busiest period, especially around Chilean holidays.
Rain is part of Chiloé's personality in every season. Spring and autumn can be beautiful and quieter, but bring proper waterproofs. Winter is atmospheric, cold, and wet, better for people who like empty roads and wood fires more than beach walks.