Cook vegan hot dogs per instructions (boil, grill, or microwave).
Heat some water in a pan on the stove, or in the microwave to the point that it is hot but you can still dip your fingers in it. Pour the hot water into a large shallow container.
Dip a sheet of rice paper wrapper in the hot water to make it pliable. Using a scissors or knife, cut the rice paper into thin strips.*
Take one strip and wrap a vegan hot dog. Repeat with the rest of the strips, rewetting them if necessary.
Repeat with the other sheet of rice paper and vegan hot dog.
Using mustard or ketchup, make eyes using a toothpick. Reheat vegan hot dogs in the microwave if necessary.
Notes
You can also cut the strips before placing them in the water, but they crack easier that way.For spring roll wrappers, it is best to make them right before serving. If you need to make them ahead of time you could wrap them individually in plastic wrap to prevent the hot dogs from sticking to each other and tearing the spring roll wrapper. Then they should last a couple of days.