Do we have free will or are our actions controlled by our subconscious?

Yes.

With this answer to your dual question, you mind will question which I answer. Thus you didn’t ‘automatically’ responded to it.

First off: ‘free will’, is a religious infused concept. 

Consciousness is the part that makes us human. The ability to plan and reflect. Other primates lack this consciousness.

What we call subconsciousness is basically our basic neural adaptability system, which creates decision trees or ‘instinctive behavior’. What animals show as behavior from instinct is what humans see in themselves as subconscious.

The first time we encounter a situation, we will evaluate, cognitively what the risks, chances, probabilities there are. When we have planned and executed actions, they become a blueprint for the next time you encounter the same kind of situation. Still, humans also have gained the possibility to have abstract thoughts and concepts, these are not behavioral. This results in the answer: we are conscious, which gives us to choose. We also are primarily a result of millions of years of evolution, which causes us to learn, adapt and behave much in the same way as other animals: instinctive.

The parts that have been ‘etched’, we don’t think about it anymore. They are an ‘agreement’ between events and your neural system, to respond in a previous acted way. If the event happens more often, the response will become automatic and will not be a ‘choice’ anymore. 

Concluded: yes, we have free will over what we are conscious about, and are controlled by our subconscious over what we don’t (anymore).