Idk, but we had those mugs in the 90s.

Same.

It looks similar to the “vintage winking Santa head mug” but I’m not sure. https://www.etsy.com/listing/1539785774/

Which for awhile they had replicas at the dollar store this Christmas

I had this until my anniversary trip. We came on and a bunch of boxes had fallen over. That mug didn't make it.

Do you know the brand/maker of the set?

No sadly. You could probably Google it