Symbolism, Imagery, Allegory
Fosco's pets, especially his mice, are fantastically creepy and borderline gross. The image of the sluggish Fosco letting his white mice run all over his body is definitely something we could have done without. Fosco's pets definitely up his ick-factor and help visually emphasize just how eccentric and weird he is.
His white mice live in a little pagoda of gaily-painted wirework, designed and made by himself. They are almost as tame as the canaries, and they are perpetually let out, like the canaries. They crawl all over him, popping in and out of his waistcoat, and sitting in couples, white as snow, on his capacious shoulders. He seems to be even fonder of his mice than of his other pets. (2.1.2.32)
The strange thing is how nice Fosco is to his pets. He actually treats them much better than he does the people around him. There's a reason for this, though.
Quiet resolution is the one quality the animals, the children, and the women all fail in. If they can once shake this superior quality in their master, they get the better of him. If they can never succeed in disturbing it, he gets the better of them. (2.1.9.46)
Fosco's ego is massive but fragile: he always has to be in control. And since his pets let him be in control, he responds well to them and even loves them in a bizarre way. Fosco's pets act as a strong visual symbol of the importance of the theme of power in The Woman in White, and they also gives us some insight into Fosco's truly bizarre (and creepy!) delusions of his own importance.