Measure the circumference of your mug: Lay down your roving onto the needle-felting mat, ensuring that it fits the length of the circumference of your mug. Use several strips of roving to create a band that is approximately 2 to 3 inches wide.
Felt the roving by repeatedly pricking the fibers all over with the needle tool until it starts to bind together and become matted. Continue along the length of the roving strips. (This process will take about 10 minutes of felting.)
Choose a coordinating roving color and use it to form a heart, the word "love," or any other chosen design. Felt the patterned roving until it melds with the felted band.
Once your piece has become one dense piece, trim off any excess from the sides, top, and bottom of the band.
Using a piece of excess trimmed felt, attach the piece onto the band in a loop.
Sew a button onto the opposite side of the band. Then, slip the cozy around your mug and fasten it closed with the button and loop.