Have you ever had a non-native English speaker tell you, "I speak in English but I think in my native language". Although I disagree with the details of that statement, I believe there are some interesting and meaningful thoughts to be taken from it.
First of all, we don't think in any language. Our minds think in terms of concepts. In some situations, we associate words to our thoughts so quickly that it might be easy to reach the conclusion that we are thinking only in terms of those words. Also, it may be easy to confuse the process of internally preparing an idea for communication with the process of actually having that idea. Even when we don't actually plan to communicate the idea to others, language is such a part of daily life that we often create an inner-dialog for ourselves. This goes the other way as well. We quickly associate real meaning (the best that we can) with the words that we are encountering. So much so, that it can be easy to believe that a new idea was the product of those words, while forgetting that our minds first had to associate a real conceptual meaning with them. So quickly we move passed our own inner thoughts and start preparing them to be communicated.
I would argue that there are many concepts and thoughts that words don't even begin to describe. For example, when we walk down the street or draw a picture, we invoke many concepts, we process (think about) those concepts, and we act upon them. And not just "subconsciously", or through "muscle memory". I mean real fully conscious thinking using the concepts that are at our minds disposal. It is not always necessary to put them into words.
That being said, often times it is necessary to put our thoughts into words. Using words allows us to formalize our minds' concepts for communication. In general, an idea has more value if it can be passed on to others. Because of this, language does have a huge impact on our thought patterns. Communication is so important in our daily lives that we probably do restrict a lot of our thinking to what can be communicated. Some people might do this more than others. Perhaps when a person attests to acting on a feeling instead of reason, they are acting on a concept or group of concepts that are in fact meaningful to them yet can not be adequately adapted into the more formal nature of language. This does not mean that they were not thinking.
I am a native English speaker. Often I've learned words from other languages that can not translate to a particular word in English. At best, there would only by synonyms for the foreign word. I assume the reverse is true as well. This is because the languages between varying cultures are derived from the use of different concepts. The concepts are not always radically different though. Occasionally I learn a foreign word that just 'fits' better than any English words I know. In those cases, it would take several English words to modify the base concept in order to communicate the same idea expressed by the single foreign word. For many of those cases, no amount of English words seem to describe the exact meaning.
The words we know and use, also help us to build up a familiarity with certain concepts. This increases how likely we are to invoke those particular concepts. For example, I recently re-acquainted my self with the word factitious. Now I find myself using it several times a day. It can actually be quite irritating. I don't really want to think about that particular concept so often. So I am left with the conclusion that my thoughts are influenced by the words I use to describe them.
This is the best argument I know for learning new words. Not just in your own language but in others as well. The words we know are tools for thinking as well as communication. They are not how we think, but they certainly affect what we think.