Leasmom, I found this info. on cream cheese....
CHEESE
Certain cheeses freeze well but are likely to change in texture. Neither cottage cheese nor cream cheese should ever be frozen. Both may lose flavor as well as texture. Cottage cheese can be kept cold and covered in the refigerator for up to a week. Its container should have a tight-fitting lid since cottage cheese easily absorbs odors from other foods. Semi-soft cheeses may be cubed and frozen individually for use in cooking. They will still maintain their flavor although texture may be altered but are excellent for dishes where melted cheese is an ingredient. Unless frozen, all cheese should be kept in the fresh food part of the refrigerator. To discourage drying-out and odor absorption, cheese should be wrapped in plastic wrap or foil. Mold that may form on cheese is not harmful. The mold may be cut from the cheese and the cheese used as usual.
I dont know how much the texture would really change since it would be between a bagel. HMMM! Id say try one and see. The cream cheese might seperate and become yucky.
Ill keep looking to see if I can find more of an answer.
Let us know if you try it....whether it works or not!