On medium-low heat in a saucepan melt butter and add flour. Whisk flour so it will blend with butter. Add milk slowly and stir constantly until all is blended and the mixture is smooth.
Add cubed cheese, garlic, chives. horseradish, and blend with white sauce. Stir constantly until cheese is completely melted and sauce is smooth, it should have a medium thick consistency. If the sauce is to thick a little milk may be added. This sauce is great for topping fried mushrooms, baked potatoes, vegetables, pasta or mixed in with ordinary mashed potatoes.