the diameter of a 250' roll is about 7". I would not recommend to freeze rolls, because it takes a long time to defrost them. As long as you don't need variable widths, I would recommend cutting the roll into sheets, package and freeze them as needed.
The curl is usually bad, but cut sheets will get flatter over the time (in the paper safe or in a box). If you plan to cut variable width sheets on demand (e.g. for panoramic prints), you should have a good vacuum easel to save your nerves.
Freezed B&W Paper will survive your fridge. Color paper at least 5 years.