Well last night Snowy was out at around 1:30am, so I opened the cage to give him a little piece of apple, which he completely ignored and then ran up my arm onto my shoulder!
So to avoid him falling, I quickly took him over to the sofa, where he spent some time exploring (with me terrified the whole time that he was going to jump off or burrow under the sofa cushions and I'd never see him again!). I guess he's had enough of being a 'ghost hamster' and decided he wants to see the world!