Mystery Up the Winding Stair by Helen Fuller Orton, 1948.
Harry Hunter and his mother have been living with his grandfather in his big mansion while his father is in Japan doing work for the government. His family has owned the mansion for a long time, and it has a small museum in it containing Native American artifacts and things relating to pioneer life, including a small log cabin built in a large room up a winding staircase.
When Harry’s mother goes on a trip to see his father, Harry and his grandfather invite Harry’s cousins to visit them: Ned and his sister Lou, and Carol, whose family has only recently moved to the area. When the children try to decide what they would like to do together, Carol suggests a treasure hunt. Their grandfather sends them on a treasure hunt to find something that he hid himself a long time ago: a set of silver spoons made by Paul Revere and a diamond. The explanation is that the grandfather is rather absent-minded and has forgotten where he hid the treasure, although he knows that it’s somewhere in the house.
A storm leaves them all snowbound in the mansion, but they are not alone. There are mysterious footsteps, someone using a secret staircase to the attic, and signs that the bed in the cabin has been slept in. The children begin to realize that someone else is in the house with them, and this person wants the treasure for himself!
Recently, I found this article, which talks about the house that was the original inspiration for the house in the story.