Sounds like you have a weak battery. How old is it? Take it to an auto parts store & have it load tested or use a multi meter with a probe on each battery terminal and crank the bike over. See what the voltage is. My guess is that you will see a substantial drop in voltage when doing this. Its taking more power to turn over that cold motor with thick, cold oil in it, so it probably wasn't that noticeable when it was warm outside. Start with the simple stuff first before tearing into the starter etc.
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