Let the cream cheese come to room temperature. Whip with a mixer, or by hand, to make it easier to spread.
Using a spatula or knife, spread about 1 tablespoon cream cheese on each tortilla, making sure to reach the edges.
Put several spinach leaves in the center of the tortilla and sprinkle with 2 tablespoons of carrots.
Roll tortilla tightly; secure with toothpick. Cut the tortilla into pinwheels by cutting it in half first, then making bite-sized slices along the tortilla until you reach the end. Lay each piece cut-side down on a serving plate.