I purchased my 06 R3 in Nov of 2010. It suffered from the common problem of not wanting tostart in cold weather. The most frequent suggestion on the forum was to increase the CCA of the battery. Some said that it improved but did not get rid of the problem.
After looking at the writing diagrams I decided to start at the battery disconnect all leads in the starting circuit. When i got to the starter, I found what I believe is the problem. The connection was very dirty and had a good layer of crud between the starter terminal and the battery cable. I cleaned up, and put a coat or two of liquid tape on it.
Last winter and this I have not had any problems cranking it up. Granted the winters in Oklahoma are much milder than in upstate New York, but I have been starting the R3 inn temps much lower than i could prior to the fix.
I am not trying to brag , just paying the group back by pass along a fix I came up