The U.S. Repeating Arms Co.--the manufacturer of Winchester rifles--has emerged from nearly two years under bankruptcy protection after its sale to new owners. The company was bought by a group of private investors and the Browning sporting firearms group of Fabrique Nationale Herstal SA of Belgium. U.S. Repeating Arms, New Haven, Conn., filed for bankruptcy protection in January, 1986, and closed for 13 weeks. A $3-million state loan allowed it to reopen. The new owners paid $8 million and assumed about $35 million in debt.