It's a big fucking continent. There's no such thing as just-one Rainy Season. Some places have no seasons. Some have every season you can imagine, every day. No matter when you leave, you'll find warm, cold, hot, fucking fffffreezing, rain, snow, sleet, storms, and gorgeous women.
Unless you want to get to Ushuaia in the dead of winter, don't worry about when you arrive, because it's always fucking cold. Or so I've heard. When I was there, one day it snowed, the next day I was running around in short, and then it snowed again.
Yes, it's a metric buttload of miles to go down and back and if you do that in 4 months you're hauling ass.
3-4 months to get down is fine. Less time and all you do is ride ride ride. More time and you're not so much *riding* as you are *fucking around in new places, and you happen to have a motorcycle.*
There's tons of info on the Latin America Ride Report thread at the top of the Latin America forum.
When you get ready to come back, stop in at Dakar Motos in Buenos Aires and talk to Javier.