Preheat oven to 350°F.
Add everything but the last 3 cookie ingredients to a large mixing bowl and mix until completely combined. Use an electric mixer, or if stirring by hand stir very well.
Add grated carrots, mix until well combined.
Add raisins and nuts. Stir with a wooden spoon.
Line two large baking sheet with parchment paper. Make cookies the size of rounded teaspoons onto the parchment paper. Flatten each ball of cookie dough with the back of a spoon so each are cookie shaped.
Bake for 12 - 14 minutes. Check sooner (8 or 10 minutes) if using a dark cookie sheet.
While the cookies bake, make your icing. Using the food processor or an immersion blender with the blade attachment, mix icing ingredients until smooth. Can use an electric mixer instead, but may take a while to remove all lumps, depending on your cream cheese.
Let cookies cool for about 5 - 10 minutes. Drizzle icing onto your cookies using either a pastry bag, a plastic sandwich bag (just cut out a corner to squeeze the icing through), or a spoon. Store left over cookies in refrigerator, if iced.