mistletoe in compost pile

This is probably a stupid question but I'm asking anyway. I am obsessed with composting. Is it okay to throw mistletoe that falls off my live oaks into the compost heap or am I asking for trouble?

I think it is O,K, mistletoe doesn't grow on the ground and the seeds should be neutralized in the composting process anyway.

Thanks, I would rather toss it in the compost than in the garbage.