A tropical climate isn't required to make up the organic matter which is eventually buried and becomes oil and gas. Furthermore, most oil isn't derived from vegetation. It's derived from marine creatures, plankton, which dies, falls to the sea floor and fails to rot because the seawater is low in oxygen and/or its buried very fast.
It is also true the Arctic was at one time found in a much warmer environment. Warm helps, as does sunlight and a lot of nutrients, a narrow, isolated, or deep ocean really helps because it tends to receive a lot of sediments and the waters can be fertilized. This leads to more anoxic conditions at the sea floor and a lot more crap gets buried which hasn't rotted and can then turn into oil.
Some oil generating rocks are incredibly old. Devonian source oils are very common. Others are sourced by Jurassic and Cretaceous sources. What happens to be t the surface today tends to be quite different of what was being deposited so long ago. But lets be clear, the one thing oil isn't made of is dinosaurs.