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It's cardboard (orange I think) clear plastic, man's head (hairless) and you moved iron filings with a magnetic pen from the back to create different hair /facial features. Something to do with spies? Google drew a blank.
Oh please don't say Etch a sketch it's not that
You'd never be able to sell one of them second hand.
I bet you could, but the purchaser is likely to be disappointed

It's similar but an older version, same principle, more of a Russki spy evil face
Looked like Ming Flash Gordon's arch enemy
I am sure the UK version was called Funny Face, and I remember the russian spy look too.
Hmm, I had one of these (I'm 55) I'll do a bit of brainstorming.
Had one too. Can't remember name tho'. Saw an updated version a couple of years ago, but rather than a bald head it had exfoliated lady-bits......

This is the one I had
I reckon there must have been so many versions the chances of me finding out are zilch 🙁 Thanks for trying though everyone
around about the 11 minute mark
looks like there were dozens of versions 'Hairy Face' and '1001 Disguisees' were mentioned in the video above. There was also 'Dapper Dan' and 'High Spy'and 'Funny Face' - and year on year the designs of them all changed a bit. So 'wooly willy' looked a bit different from one year to the next. The official ones were made in the states but I guess anyone with a vac-forming machine could do their own knock off versions too. But you could do image searches for any of those names and the one you're remembering might pop up.
The original versions were made by a company called Smethport. But whether the ones we got here in the UK were Smethport's versions or local / hong kong knock-offs I'm not sure.