When the 'toy room' door closes. And if they escape the room and get caught, they die. Not animated, late 80's I vaguely remember christmas, and a new toy arriving

Try

The Christmas Toy (86)

Toy Story's premise seems similar to this earlier special by Jim Henson.
The toys in the playroom are free to move about when no one is around, but they must remember never to be seen, or they will be frozen forever.
Last year's favorite toy ,Rugby a stuffed tiger insists on leaving the playroom on Christmas Eve, and goes down to the Christmas tree. The other toys try to stop him. He goes anyway and manages to unwrap this years toy, Meteora, Queen of the Asteroids who doesn't seem to realize she's a toy... (sound familiar yet?)

Rugby and his friends in the playroom returned in a series called
The Secret Life of Toys

Thank you so much, I thought it was a Henson creation!