.  
That all frost, ice and snow has been removed, particularly on lift-producing surfaces. If you leave hoar frost on the fuselage (only if it can be seen through), beware of flying into cloud

where more will stick. It must be removed from places where its dislodgement could cause ingestion, e.g. engine cowlings.
.  
Check any particle separators as water seepage may have frozen inside the engine, resulting in abnormally high N1 and JPT readings (in a turbine).

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That the skids are not frozen to the ground. On a solid surface, you might be able to rock it using the tail. Otherwise, use the pedals with a little collective just before takeoff.

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Unstick windscreen wipers and moving parts (including rotors and propellers) by hand, or you will strain the motors.

.  
That control linkages and
movement are checked.

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That pitot heat is checked by hand—don't just accept a flicker on the ammeter.

.
Water drains are not frozen.

.  
That carb heat operation is
checked.

Static becomes problem when it’s cold, as snow and air can be very dry and therefore good electrical insulators – a helicopter can retain its normal static charge quite efficiently when landing on snow (before refuelling, remove your survival kit, so if it blows up you’ve got something to wear after you’ve warmed your hands in the fire).
When possible, the first start of the day should be an external one. With a turbine in cold weather you can expect a lower achieved N1 before light up with abnormally high JPT peaks, eventually settling down lower than normal. Oil pressure will be slow to rise, but high after starting – do not go above ground idle until pressures are in the green and will stay there as you increase the throttle. Temperature, on the other hand, will be very slow to rise at all, and you want the transmission to be at least indicating something, which will mean the engine oil is OK as well, as it gets hot quicker. Allow the electrics to warm up, too – even the knobs can get brittle.
Don't wind up to flight idle too quickly in case you spin or yaw on the pad (the cyclic should be central), especially if there’s an engineer on a ladder doing a leak check (be careful with rotor brakes as well). If the machine has been frozen to the ground, one skid may come free first and cause dynamic rollover. If it has not already been freed, pull collective until ready to lift and crack it free with a little controlled pedal movement, though on a big machine you might want to use engine torque for the same effect, otherwise you might bend the tail boom. You could also try gently circulating the cyclic, or pulling down on the tail boom before starting if the machine is light enough. Taxi slowly with caution if the taxiways are clear of snow. If not, taxi higher and slightly faster then normal to keep out of the resulting snow cloud. If you have wheels, act as if you have no brakes.