Not riding much in Alaska

I have an 05 Rancher with electric shift. Over the past few winters it has given me trouble when it is below freezing. When it is cold outside the Neutral light will not come on so I can’t start it. I can shift into all gears including neutral but the light won’t come on. Once I have warmed up the entire machine above freezing the neutral light will come on. I don’t understand how the neutral light is related to the temperature. It is not a battery problem. I have also tried replacing the starter and neutral switch.

I will place this question General Maintenance section once I figure out how to do so.

Thanks,
Wes

ps. I have a small flower farm in Alaska. I need to use the ATV to plow what little snow we have on top of the flower beds to insulate them for the winter