I guess it is fairly common in siamese cats. Isn't a Snowshoe a relative of siamese? I took my Himalayan to the vet for her 12 week check up and the vet commented that she had slight Nystagmus like some siamese do. When she looked at her a certain way, her eyes shook but I have never seen her do it myself. But my vet didn't seem to think it was anything to be concerned with and she knows I am pretty psychotic when it comes to caring for my babies so she would have told me if it was someting to be concerned with. But you can do a Google search on "Cat Nystagmus" for more info.
I spoke to my Vet. about my Siamese's eyes that shake (male), it's sister's eyes do not shake. But they are not full bred Siamese (hope I'm spelling that right) they are part Tomcat. The Vet. says that it is a trait of Siamese and the sister just did not inherit that trait.
The vet just mentioned to me that my Himalayan cat's eyes move back and forth, instead of staring straight ahead. She said it's common in the breed. My cat has seen veterinary opthalmologists many times, and they've never commented on it, so it must not be of concern. I wonder if having nystagmus affects their vision in any way. Anyway, if the vet's not concerned, I wouldn't be, particularly if it's common for your breed. It's just funny that all the specialists my cat's been to, and all the years I've had her, it's the first time I heard about it, just the other day.