This question is about normal vanilla minecraft in survival mode. I've noticed that mooshrooms seem to only spawn on mushroom islands. Is my guess correct, or is there another set of parameters in which they can spawn?
They will spawn only on mycelium biomes, and the only mycelium biome in vanilla minecraft is a mushroom island. Also, as KenzoEngineer said, the only other way to spawn them is through commands and spawn eggs, which are not natural in vanilla survival.
You are correct. Mooshrooms can only spawn on mushroom islands. The only other ways would be to spawn them in with spawn eggs, or using the
/summon command in a format like:
You can of course bring the Mooshrooms away from the island onto the main land with wheat or leads.