My R3 is one of the ones that didn't like to start in the cold, and not just really cold weather, I had problems in the low 50's. I went to the Odyssey 545 and then the 625, but it didn't fix the problem.
After multiple stays in the dealer's shop they said they had found the problem was a crankshaft sensor was out of spec and that the change in temperature was enough to cause it to fail so the bike would not start. I was a little dubious, but the bike did seem to start ok. Of course, it was March and the weather was getting warm at that point.
The problem start reoccurring this September. The dealer replaced the oil with a lighter oil, and also replaced the Odyssey battery with a stock battery and the problem seems to have gone away. I put the Odyssey back in and the problem came back. So I'm still dubious here, because this problem occurred with the original stock battery and two Odyssey batteries and I wouldn't think lighter oil and a return to a stock battery would cause the problem.
That being said, it has started just fine in the low 30's now and I haven't had any more problems.
I did have some remote LED engine lights wired directly to the battery that the dealer said he thought was draining the battery and causing my problem. However, those were not installed when the original problem occurred and were only put in place after they initially said it was fixed, and the problem still occurred even after me disconnecting them with the Odyssey 625 in place. I haven't wired them back up with the latest battery yet and will probably put them on a relay.
Anyway, I can feel your pain. Having a bike you can't depend on is no fun. Right now mine is finally working, but it will take some time to really come to trust it. I was considering the spare battery solution myself before this last go round, and if it happens again that is probably the solution I will implement. That or trade it in for a Thunderbird Storm.
Good Luck