I have a couple cheap battery powered motion sensor lights outside my house and have them positioned, after some trail and error, to where passing vehicles and tree branches no longer set them off. But lately they seem to be on a lot. Could the colder weather be the cause of this?
yes.
temperature changes in front of the sensor trigger the light. a cold wind could chill something and this act as a triggering.
An anecdote from my past : Had a separate workshop/garage where I kept my restored '71 Charger. It had a motion sensor wired into the ‘professional’-level security system. The shop was not heated, and was in Central Oklahoma (not terribly cold, per se).
Four times, I was called by Sheriff’s Deputies, as per contract, that my alarm had gone off, which meantt I had to go home ( hour-and-half drive from work at Trauma Center, a BIG deal) to ‘clear’ the alarm situation. Three times the sensor was replaced, and everytime it false-alarmed whenever temps got towards 10-20 degrees Fahr. I was told it was common, per Deputies, but I would start getting charged for anymore false alarms. Reasonable, but alarm company denied temp affected performance. Pure BS, but that is what I went through - a shop where nothing could move on its own, yet triggering an alarm-signal purely based upon prevailing temps of unheated area.
I ended going with more dogs and a gun-happy neighbor -v- electronic monitoring. MUCH more reliable than motion sensors, but YMMV (and situation, of coure)
I definnitely showed it was temp and not leaves blowing around in a well-sealed shop - but company denied it wholeheartedly. It was said to be impossible, yet there is a clear record of false alrams (or false ‘positives’) due to low temps via personal video of area when alarm triggered. (I did get full refund without any dispute when company shown the vids and results of thier ‘awesome products’.
YMMV, and just sayin’…
Also had same isssue with a motion sensor on a driveway-cover of four cars. The colder it was, the more-likely it was the lights would come ‘on’ from the one snesor, even if nothing was moving anywhere near the sensor. It often stayed on all night, so it got trashed. Cheapo sensor, so no big loss, but lesson hitting me over head yet again 
I can say that there was a medium sized pecan tree about 200’ feet away and not in the ‘view’ of the sensor. When windy, there was no difference in the sensor being in ‘on’ or ‘off’ cycle. Temp is only variable I could find in that situation as well.
Might be relevant, maybe not. Hope it helps, though
‘Motion sensor’ is a misdirect. They are actually heat sensors. And they don’t work as well in lower temps.
Anecdote; I ride motorcycles and have a ‘motion sensor light’ in the mud room between the garage and house.
When I come home on a day where I’m all covered (full face helmet, jacket, gloves) I can walk right up to the light and it doesn’t come on - until I remove a glove or the helmet.
Thanks. Guess I’ll wire a porch light to the new porch and retire the motion sensor lights until spring.