What effect does cold weather have on helicopter performance?
Cold weather definitely affects the performance of helicopters (as it does all aircraft), because it affects the density of the air they move through. 

I will ignore icing so let's assume dry air.

The lift equation is:

$$ L = \frac{1}{2} \rho V^2 S C_L $$


$L$ = Lift


$\rho$ = density of the air. 
$V$ = velocity of the aerofoil (rotor)
$S$ = the wing area of the rotor 
$C_L$ = Coefficient of lift , which is determined by the type of rotor and angle of attack.



As you can see, lift is proportional to the density of the air and since density at any given altitude is inversely proportional to the temperature, the colder the air, the more dense it is.  So, for a given rotor, spinning at a given speed at a given altitude, the colder the air, the more lift is produced.

Engines also operate more efficiently when the air is colder since the density is higher and the charge of air/fuel introduced into the engine is greater. (See here for more information.
 Of course, this does not apply to your RCH apart from some effects on the efficiency of the batteries and motors (which may perform more poorly at lower temperatures).

So in general, the colder it is, the higher the performance.  In most helicopters, the difference in performance on a cold, dry winter day is very noticeable and much better than on a humid, hot summer day. 

It's also worth understanding the properties of air.  The colder the air, the lower the dewpoint so the less moisture it can contain.  Moisture in the air also lowers peformance.



The problems you encountered with your RC model aren't problems with helicopters in general.

Colder weather does not make you more susceptible to vortex ring state (aside from some minor side effects): You would still only descend into the vortex if you did not pilot the helicopter correctly. (Note that you cannot enter vortex ring state with the rotors stopped since they are not producing a vortex.  Also note that on a real helicopter, if the rotors ever stop, they will not start again no matter what you do.)

BTW, I'm being pedantic, but helicopters do not have propellors.  Technically, they are the same thing, but asking a helicopter pilot about the propellor annoys them, even if they don't show it.  It's as bad a calling a helicopter a "chopper".  Only Arnie and Chuck get to call helicopters "choppers".  And that's only because helicopter pilots are universally weedy and would get stomped by Arnie or Chuck if they argued.