If it spins freely then you're good to go.  I can conceive of a motor tightening up from the cold, but I'd have to feel it turning to believe it.

Your batteries don't want to be too cold -- I'm not sure what the low point is, but I'd leave them in my nice warm car until it was time to fly.

Truly oddball cases aside, if you're concerned about operating temperature you can (and possibly should) partially block the cooling intake on really cold days.  I know people have mentioned it here, but I've never had occasion to.

The only moving part in the motor susceptible to the cold is the grease in the ball bearings.

This is probably true of the motors we use in our hobby, and the temperature ranges that we fly at.  Over aerospace or industrial temperature ranges (-40 to +85C) I've seen things bind up because of differential expansion or contraction of the parts.  That's usually been with parts that are way bigger than our motors, and had preloaded bearings, which is not something you want or need in our motors.  But it is a thing -- so if you happen to be flying in Alaska in the winter, or if you've been invited to stay in the Antarctic from May to September and brought a plane along, keep it in mind.

If you did fly in the cold, and you couldn't manage the plane temperature by keeping it in your car or wrapping a towel around the nose between flights, there are greases (generally both more toxic and more expensive) that work over wider temperature ranges.  A mechanical engineer I know at a prior sorta-aerospace job called our go-to grease "cocaine grease" because of the color and the cost per ounce.  I never asked how he knew...

Your note made me grin as I remembered at -57F a Cobra Attack Helicopter (AH1P) Turbine engine start, as it spun up-- radially blew it self to junk.......seems a shaft speed of 100,000+ RPM needs a bit of lube that probably is a lot like your Cocaine Grease.. I learned that HS bearings do not like to skid, stall, and gall

If you were cursing any design engineers, that was my tribe.  My experience with failures at cold mostly involve looking into the window of an environmental test chamber and saying "it no workie" -- not actually having to, like, get cold.

And we only had to design for -40C operational, -55C storage.  Although we would quietly test all of our junk by doing an overnight cold soak at -55C, and then immediately warming it up to -40C and turning it on.

(I like -40, because you don't have to say whether it's -40C or -40F.  BTW.  Cuz I'm a nerd.)