Generative AI models offer many possibilities for text creation and transformation. Current graphical user interfaces (GUIs) for prompting them lack support for iterative exploration, as they do not represent prompts as actionable interface objects. We propose the concept of a composable prompting canvas for text exploration and iteration using dynamic widgets. Users generate widgets through system suggestions, prompting, or manually to capture task-relevant facets that affect the generated text. In a comparative study with a baseline (conversational UI), 18 participants worked on two writing tasks, creating diverse prompting environments with custom widgets and spatial layouts. They reported having more control over the generated text and preferred our system over the baseline. Our design significantly outperformed the baseline on the Creativity Support Index, and participants felt the results were worth the effort. This work highlights the need for GUIs that support user-driven customization and (re-)structuring to increase both the flexibility and efficiency of prompting.