So, after sleeping on it and doing a little more Googling, I figured out the wiring for the Viper remote. Under the Can-Am's hood is the winch relay, with 3 wires on the low voltage side:
1. Green, which reels the cable in when voltage is applied.
2. Black, which is the ground.
3. Light blue, which reels the cable out when voltage is applied.
On the Viper's wire harness, there are the following cables:
1. Black with a ring terminal - system ground.
2. Red and yellow wires soldered to an inline fuse - system positive.
3. Black with 2 bullet connectors - cable in voltage when "IN" button is pressed.
4. Green with 2 bullet connectors - cable out voltage when "OUT" button is pressed.
To turn on the system, press both IN and OUT buttons for 3-5 seconds.
I wired up the system's power leads to the terminals under the Can-Am's hood. On reflection, I probably should have wired them to the switched terminals under the dash instead. That way, the system would lose power when I turned off the key. As it is, I have to manually shut it off by pressing the button on the main unit. It's supposed to automatically turn itself off, but I haven't witnessed that yet.
I wired the system's IN and OUT wires to the appropriate relay wires using in-line taps. (System black to relay green and system green to relay blue).
Once I was sure it would work, I shortened the cables and screwed the unit to a convenient mount point. See picture.
Thanks to those who went before and pointed the way!
Happy Trails,
Joe