The pig cozy is a little larger to fit on a thermal travel mug.
These are both worked as a rectangle using HDC for 5-7 rows depending on your yarn type, in the final row work the ears by measuring about mid-point, stop turn back, ch.2, HDC 3, turn, ch.2, HDC 2 decrease by one, turn, ch. 2, HDC 1 decrease by one, turn, slst down the edge of ear to rectangle, HDC 4 sts. make second ear same way then HDC to the end of row and tie off.
For the loop, at about mid-point attach yarn and work 10 chains, skip 3-4 sts, then tie off. Find some buttons for eyes and one button for the loop. For the pigs nose, ch.4, slst, in the center work 8 HDC, slst and tie off leaving a tail. Pull through to back side and tie a knot to hold in place. Sew on eyes and secure nose from the back. Sew on button to the opposite side for the loop closure. For the fox, work the same rectangle only the first 2 rows are worked in light color yarn, change color for final 4-5 rows, work the ears in the same way as for pig. For the snout, tie on same color as face between ears (oops, my snout and eyes are not lined up properly, but that's OK, still cute) on the color line, ch.2, work HDC for 3 st, ch2, turn, decrease 1 st, ch. 2, turn, work 1 HDC, tie off leaving a tail. Pull tail to back side and tie off. Thread black upholstery thread and satin stitch nose pulling to back side to secure. Add buttons for eyes and loop closure, same as for the pig. All sewing is done using the black upholstery thread and a large eye wool applique needle.
I am sure you could easily make other animals with this basic instruction, maybe a cow, or a monkey? See what you can create with just a little bit of leftover yarn.