Winchester, 32, spent all of last season in the AHL, totaling 27 points in 37 games with the Milwaukee Admirals. He last played in the NHL in 2011-12, when he had 10 points in 67 games with the San Jose Sharks.
Peckham, 25, had a minus-1 rating in four games with the Edmonton Oilers last season. He also spent time with the San Francisco Bulls of the ECHL and the Oklahoma City Barons, the Oilers' AHL team.
I don't have a crystal ball. Predicting is a real complicated thing. If we stay healthy, have enough depth and get the good goaltending we think we're going to have, you can go all the way. But a lot of things have to happen. There's going to be a lot of teams that think the same thing. Everyone made deals. We're all are optimistic about where we'll end up.
— Rangers general manager Glen Sather after being asked if he's constructed a team that can win the Stanley Cup before their 4-1 win against the Predators on Monday