Hello Octopus and welcome from Virginia. I have a 2014 R3T and am on my fourth battery. When mine gets cold, say around 27F, it will not turn over properly and throws a code (check engine light on). Oftentimes, it will not start and the GPS (Gear position sensor) goofs up and the neutral light will not illuminate. Therefore, I must raise the kickstand and try again to start it as if it is in gear. When it does start this way, the check engine light stays on for 3 normal starts afterwards before it extinguishes. Or, it goes out after I disconnect and reconnect the battery. The cold temperatures drives me nuts when I can't start the bike because of it.
Another issue I have is that I do not deep clean the bike as often as I should. The battery cables are not up to snuff as it is and when they become dirty or corroded, they make it hard to start, especially in the cold. I have replaced my negative cable with two and that worked for a year and a half, now its time to replace them again and the positive as well. I am also going to upgrade my starter to a Toyota unit. Several others here have done so with great success.
Good luck brother!