Can mooshrooms breed with cows?
Snapshot 12w07a removed the ability for mooshroms to breed with cows.
According to the Wiki, mooshrooms can only breed with other mooshrooms. If you shear the mooshroom, it becomes a regular cow again, to which it can then breed with other cows once again:
A mooshroom cannot be bred with a cow, unless the mooshroom has been sheared.