Oil Wells produce Oil in each of the climates except Toyland.
OpenTTD keeps the behaviour of the original Transport Tycoon Deluxe, where temperate oil wells never increase production. They only decrease production until they run dry and close. New wells never spawn after year 1950, so wells continue to close until they're all gone. Because of this, some players ignore Oil Wells and wait for Oil Rigs to appear.
In Temperate Climate without NewGRF Oil Wells will never increase production and only decrease until they run dry. However in sub-arctic and sub-tropical climates, the wells increase and decrease production like other primary industries. New wells never spawn after year 1950.