Place cauliflower florets in a food processor; pulse into grains the size of rice.
Combine hot water and saffron threads in a small bowl; let stand for 3 minutes to infuse.
Heat 2 tablespoons olive oil in a paella pan over medium heat. Add sausage; cook and stir until browned, about 5 minutes. Stir in zucchini and onion; cook for 3 minutes. Add saffron infusion, carrot, garlic, and cayenne pepper; cook for 1 minute.
Stir cauliflower "rice" and artichokes into the pan. Cook and stir until slightly softened, about 3 minutes. Pour in stock; season with salt and pepper. Bring to a boil; reduce heat and simmer until most of the stock is absorbed, about 10 minutes. Stir in snow peas; simmer until all stock is absorbed, 3 to 5 minutes more.
Remove paella from the heat and drizzle remaining 2 tablespoons olive oil on top.