Neutral and hostile mobs in the Nether don't spawn when I switch from peaceful mode to easy/normal/hard in the Overworld and enter the Nether afterwards. And I'm not entirely sure, but I think that this also happened after I had left the Nether - it was night outside and no hostiles were spawning.

And yes I'm 100% certain that I had a harder difficulty turned on, my hunger bar was depleting.