OK, some basic facts:
Generally speaking, the atmospheric model shows that the temperature decreases as a function of altitude up to the tropopause at a rate of about 2 degrees Celsuis per thousand feet.
The tropopause in this ISA (International Standard Atmosphere) is at about 36000ft and the temp is -56.5deg Celsius.
Most routine jet aircraft operations take place between 30,000 and 40,000ft and are expeosed to these temperatures, so, no, they are not an issue.
As I said, that is the ISA.
In reality the tropoause altitude varies with latitude, and will range from ~25,000ft at the poles to over 50,000ft in equatorial areas.
In reality also, the temperatures experienced can be much colder, with -70deg C not unheard of (in fact iirc BA38 whichcrashed short at LHR a couple of years ago, had experienced temps even colder than that).
Some aircraft have environmental envelopes that specify minimum temps acceptable, (A320 family has a -70deg C limit from memory).
Next, about icing.
The amount of water that can be held in a given volume of air varies as a function of temperature. The warmer the air the more the water it can hold. It is deemed that below -40deg C (or F - the temp scales meet here), that the air can not contain enough moisture to cause icing, and we dispense with anti-icing precautions unless in descent. In the ISA model -40deg C occurs at about 28,000ft.
You will not get the same amount of icing all the time at a given temperature, it depends on local conditions. At times the severity of the accretion rate can be a problem even for the best protected aircraft and descents (or climbs) may need to be sought from ATC.
It sounds like the Herc was in severe icing rather than the temperature being too cold.
Hope that helps.