Aircraft such as a Cessna 172 are routinely flown in cold conditions. The regulatory objective is to avoid all known icing conditions. The practical objective is to avoid all likely icing conditions. Aside from that the aircraft has very basic anti-icing tools.
Carburator heat is one, but one must be aware that carburator icing happens under conditions, including warm and humid days and is different from airframe icing.
Pitot heat and in many light aircraft, static port heat, are used to maintain operation of basic flight instruments, namely the barometric altimeter, the airspeed indicator and the vertical speed indicator.
In my experience flying in the northern part of the US and throughout Canada, I have experienced icing which overwhelms pitot heat, as well as other anti-ice systems including prop heat and wing anti-ice system. (Think 1" a minute of clear icing!) Also improper use of boots on the wings can lead to the ability of the expanding boots to shed ice, when the boots have been applied prematurely, causing an expanded shell of thin ice to form which does not shed, and has further accredtion of ice.
There are generally two elements for airframe icing: moisture and temperature.
Moisture is pretty obvious. If one stays out of precipitation and out of clouds, the amount of moisture in the air is locally less, and while a trace of ice may form, in the course of a flight it may also sublimate. Yes, it is possible to pick up very small amounts of ice even in clear air, with no visible moisture or precipitation. But it doesn't happen that often.
Temperature is the other component. Generally an aircraft will shed ice when just slightly above freezing. If flying in conditions with a temperature inversion exists, sometimes climbing 1000 or 2000 feet will be enough to stop accumulation and start shedding ice. Usually higher means colder. And the good news is that colder temperatures may also reduce ice accretiation rates.
For example on one trip between LGA and BOS, at 4000, there was moderate ice. Climbing to 8000, and colder air, reduced the icing, and when dryer conditions were experienced enroute all accumulated ice was sublimated.
When the temperatures are very cold (-30C) there tends to be little ice accumulation. The air contains very little moisture at those temperatures, and while ice can accumulate, it infrequently does, compared to temperatures of -5C.
Propellers are a concern in that they too loose efficiency with ice accumulation. Flexing the prop with power and RPM changes helps shed ice. Some props will have nozzles which sling out alcohol, and some have heated pads which are electrically powered. A asymetrically iced prop can destroy engine mounts and has been the cause of more than a few inflight losses of engines, where they have physically separated from the aircraft.
One additional technique implemented by many pilots who are concerned about icing, is to coat the prop with an ice-shedding substance. A thick silicone spray is used, and it is not slung off by a spinning prop, at least rapidly. Changing RPM or prop pitch flexes the prop and can also aid in keeping the prop clear of ice, and reasonably balanced. Some people have used automotive silicone spray, but it does not work as well.
A more difficult problem operating in icing conditions, is being able to see. Some aircraft have poor or virtually no window de-ice. The Cessna 172 is a good example. More than once I have had to slip on short final to effectively see out the side window to recognize the landing environment. A product called RVR, which works similar to Rainx keeps a hydrophobic state on the windshield and helps enhance ice shedding, as well as liquid water shedding. It is a window treatment and is simply routinely applied, rather than episodically.
Finally, there is no substitute for more power. It can get the aircraft up through a layer where ice is accumulating, and it can also keep up a good climb rate when the aircraft is heavy with accumulated ice. Flying a Cessna 182 vs a Cennsa 172, can reduce the impact and accumulation should unexpected icing conditions be encountered. All the time trying to climb at Vy (where Vy keeps dropping) provides more frontal area to accumulate more ice. So higher power lowers the nose, and also gets one up higher faster, or helps a plane heavy with ice.
Just one anecdotal story...when young and learning weather flying, we would jump at the chance in the fall, when there were brisk mornings, and the freezing level was about 2000, and there was a scattered layer of lake effect clouds. Into the cloud, and we would get a layer of ice, and then out of the cloud, we would watch how it would sumlimbate. Too big of a cloud with ice, and we would climb over the tops and the accumulation would stop. When we were going to land we would drop below the freezing level and the ice would all shed off. I do not recommend this method unless suitably skilled, and you have assured yourself that your operation is regulatorily acceptable.
So winter flights where icing is a possibility should be taken with ice countermeasures, such as silicone on the prop and even on the wings and control surfaces. Not only a through briefing, but more importantly a good understanding of weather specific to winter flight is essential. Changes in altitude either up or down can take the aircraft to better conditions. If clouds are prevalent at lower altitudes, flying at higher altitudes may keep one entirely out of icing conditions. Route deviations, particulary due to orographic and coastal conditions may be in order.