Does a single inbred mouse strain (e.g. B6) have SNPs - (Aug/09/2013 )
Genetic variation shows up on Ensembl but I'm not sure if these data represent cross referencing with other inbred mouse strains.
Inbred strains should be fully homozygous in theory. Of course you can't stop sporadic mutations from happening, but they will be hard to find if you need them (i.e. to tell a one alelle from the other). Better to cross with different strain then.