The short answer is yes, keep everything. Traditional upholstery materials, such as horsehair, used in pre-40s furniture can be very long-lasting. No matter what the age, I recommend re-using as much of the original padding as possible as it defines the chair’s shape and results in much less work and expense. Do keep the original layers even if you have to replace everything, as they provide a valuable guide to follow when building those layers back on with new material.