Psycholinguistics research has repeatedly shown that the amount of influence is minimal, amounting to, in general, forcing you to pay attention to certain aspects of the world more so when you're
describing using language than when you're thinking about things in other ways. E.g., you notice color differences more quickly or more accurately when you have to choose between two words that your language could have, than if you were picking a tee-shirt. Or you're more attentive to left and right orientation if your language has words for left and right
when you're talking about something positioned relative to your body, but if you're just trying to navigate somewhere or looking for something, your language doesn't affect your thinking.
This effect is precisely what you'd expect, ofcourse, because you get it for absolutely everything else. If your culinary habits involve avoiding high fructose corn syrup, when you're looking for food you're going to be quicker to notice the presence of HFCS than if you're just talking to someone and they mention the corn industry's current HFCS production rates or whatever.
The generalization: when some cognitive task requires that you pay special attention to something, you will. Language is not special in this regard.
And that is how language influences the way we think.