Yes, your stats affect your cooking success, as well as the cooking kit you use and level of food you cook.
You can glance on your chances to cook
here.
In short, your dex and luck heavily affect the result (It counts total stat with bonuses), as well as your base level. You can skip cooking exp. Cooking kit adds a bunch. First 2 (Outdoor and Home) cooking kits are buyable after you finish cooking quest (You need to finish it anyways to get level 1~5 cooking books access). Fantastic cooking kit ALWAYS gives 100% success, so if you'll get those keep them for high level foods (8~10).