On a 650V2 you should start with the "plungers" aka chokes. They stick or hangup. I'm running a little rich now on mine and I'll be pulling the plungers again.
At 2000mi if the valves haven't been adjusted then they probably should. It's a PIA job on a V2 in IMHO.
Sync'n the carbs is pretty easy, helped my machine run a better.
I would also use some Seafoam in the next couple of gas fill ups. Your carbs might be a little dirty.
FYI: My 650v2 has started in weather as cold as -10F. So get yours tuned up and running good and winter shouldn't be a problem. I also give it a little throttle to start sometimes, seems to help.
05 650V2 LE, 09 550H1,04 Arctic Cat 50
"Every man dies. Not every man really lives" -William Wallace