The .303 Savage is about the same power as a .30-30 Winchester. The Winchester 190g Silvertip loading has a muzzle velocity of 1890 fps. This would fine on deer out to about 125 yards or so. The bullet won' t have a great trajectory with the slow muzzle velocity, but due to it' s relatively heavy weight for the diameter - it should penetrate very well.

The Savage 99 is a great lever action. Your rifle should be fine as long as you aren' t trying to hunt clear cuts or fields.