Winchester, 32, has 16 goals and 30 points in 55 games this season with Rockford of the American Hockey League.
A second-round pick (No. 35) of the Edmonton Oilers in the 2000 NHL Draft, he has 37 goals and 68 points in 390 NHL games with the Oilers, Dallas Stars, St. Louis Blues, Anaheim Ducks and San Jose Sharks.
Connelly, 27, has played 50 games this season with the Iowa Wild of the AHL, leading the team in assists (27) and points (32). He ranks second among team defensemen in goals (5) and power-play goals (3).
Connelly will report to Rockford, where he spent parts of four seasons from 2009-12.