How does the environment influence farming?

According to currently available sources, farming is not affected by any external factors (soil type, rainfall, biome, temperature etc.). The only factor that affects plant growth is the growth rate of the particular crop. Toxic Tops require roughly 280 growth cycles, whereas Wheat only requires 27 cycles (a growth cycle represents the interval at which the game calculates growth, and is 20 seconds).

Taken from the Starbound Wikia site: http://starbound.wikia.com/wiki/Farming

Obviously, as the game is still in beta, there is room for this to change.

Update Oct. 2015 (Stable development branch): Crops will not grow in the absence of rain and/or of a player character.

Even though this is an update, I'm submitting this as an answer rather than a comment because the answer has changed: yes, the environment does influence crop growth. For some elaboration, please see my answer at this link.