1. Drawing the Hat
Draw two basic paths and fill them with Linear gradient (red to darker-red).
Create a shadow path similar to the image on the left. Pick the top part of the hat. Copy and Paste the hat in Front (Ctrl+F). Choose the copied path and the shadow path. Press the Alt key and choose Intersect shape areas in Pathfinder palette.
The path should be similar to the image on the left. Repeat the same step to create another shadow path for the bottom portion of the hat. Fill these 2 shadow paths with Linear gradient (red to darker-red) From the Transparency palette, pick Multiply.
Using the Pen tool, draw a rough path and fill it with the grey colour. Navigate to Effect > Distort & Transform > Roughen.
Enter the following setting s for the Roughen Options: Size=8%, Detail=95/in, select Corner points. To see the result click on the Preview check box.
By holding Alt + drag (you can also use Copy & Paste) create a copy of the grey path and fill it with white. Scale the image a bit and place it slightly above the grey path. Choose the top portion of the hat and its shadow. Then bring them to front by means of Object > Arrange > Bring to Front (Ctrl+Shift+]).
Using the Ellipse tool create a circle and repeat the previous step to create the furry ball.
The final illustration should look like this: