Paul is right, it's an old-fashioned thingie with a small mirror and clothes brushes. You can see it quite clearly when Ennis leaves the Twist house:
In this one, you can see the object and the hat behind Ennis pretty good:
I'm wondering about this holder for clothes brushes. To me it looks misplaced. Not a thing you'd expect to see in a house so stark and sparsely decorated as the Twist house. I perceive it more as an item you'd find in a house in town, rather than on a farm. I mean, who needs to brush their clothes before leaving the house to go and work on a farm?
Maybe it's a wedding gift? It could very well be the type of gift that people in the country with little money gave as a gift to give the new home a certain "air".