You did not say whether your Uberti is the high or low-wall type. The high-wall is offered by the factory in .303 British, which is one of the calibers chambered in the original Winchester High-wall rifles. The High-wall should certainly be safe with the .44 Magnum, but the low-wall, while suitable for .44 Special pressures, would not be a good choice for the .44 Magnum, which operates at pressures of the same level as the .303 British. A good gunsmith can easily ream your chamber for the longer round, but should be aware of the limitations of the low-wall action, which does not provide as much support to the breechblock as the high-wall, and therefore is not suitable for the higher pressures.
PRD1 - mhb MIke