I already winterized the sprinkler system itself and I am wondering if I need to winterize these copper pipes as well. Should I open up the bottom plug to drain the verticle pipes? I live in the Northeast of the USA. I don't have a bleeding valve inside the house that's close to these outside pipes.
Yes, you need to winterize them. That looks like a backflow-prevention device, which prevents water from the lawn from flowing back into the city pipes (in the event of a loss of pressure). Typically, when I lived in TX, my winterization procedure was to shut the inlet valve (the green-handled valve on the right side of the device in your picture) and turn the screws on the short stubby pieces 1/2 or 1/4 turn and drain the water from the backflow device itself. Turn the outlet valve (green-handled valve on the left of the device) partway closed. Wrap the piping in foam insulation, and possibly wrap the backflow prevention device itself in a towel or shirt for the few nights it dipped below freezing.
Given that you're in the Northeast US, though, you should have a shutoff valve / drain somewhere inside the house. Any piping prior to the inlet valve will still have water in it unless it's drained, and that portion of the pipe from the house to the inlet valve will freeze if it isn't drained. Once you find the shutoff, open its drain if it has one, and open the drain on the short vertical piece below the backflow device. Once all the water has drained you can close the drain on the short vertical piece. In the spring, close all the drains and open all the valves.
It may be a poor design, but the important thing is to make sure that any pipes exposed to the exterior are not full (or close to full) of water. The only way to do that is to drain the water in the system as part of the winterization.