There have been mice characters seen in several books of Dr. Seuss.
Mr. Mouse is one of Sam's animals; he appeared in the Dr. Seuss book Green Eggs and Ham. He is seen in a house with Sam. In the TV series of the same name, he is named Squeaky (by Sam) in a similar role; however, Squeaky is a French convict, imprisoned for stealing some cheese to feed his starving daughter, and is a parody of Jean Valjean from Victor Hugo's novel, Les Miserables. He even references the musical by explaining his backstory through song - though it is completely overlooked by Sam and Guy, since all they can hear from him are loud squeaking noises, thus explaining his name. He is also voiced by Daveed Diggs, who played Lafayette (and also Thomas Jefferson) in the original Broadway production of Hamilton.
There is a mouse seen looking at the Guy in a Old Hat and another mouse who cuts a telephone wire that Joe and his Brother were using and a 3rd mouse sleeping in Ned's bed with a dog and cat on One Fish Two Fish Red Fish Blue Fish. It's unknown if it's the same mouse that was seen 3 times.
Two mice are seen ice skating on ice and later are carrying ice as seen in the book I Can Read with My Eyes Shut!
Two mice are seen on How the Grinch Stole Christmas! (Book) 1 in the house looking at a crumb on the floor after the Grinch had left up the chimney and another looking at another crumb in another house from which the Grinch had left.
A mouse on Hop on Pop is seen standing on a little red house then later carries the house away with him.
There are 6 mice on Dr. Seuss's ABC who are humming in the woods as the moon shines in the sky. Their names in the Living Books books version happen to be Mario, Marvin, Mary, Melinda, Mike, and Minerva.
The is a mouse who is friends with is a bird in the book In a People House.