I am slightly bemused by the question and most of the answers.
If this is your qualifying cross country you have had it drumed into you to stay out of cloud. Moreover you will not be allowed to go on a day where there is a risk of your entering cloud (or exceptionally very moist air with below freezing conditions).
In reality it is extraordinarily rare to accumulate ice in clear air and even then the accumulation will be very slow. I have had it happen once at night in VMC (in fact very good VMC). I think it was a combination of rapidly cooling conditions (as night set in) precipitating water vapour and a cold soaked airframe. The aircraft was FIKI so it was not an issue and only a few short runs of fluid were required to deal with a problem that probably would not have been much of a problem even without FIKI.
In short if your instructor says it is good to go you will not have a problem as long as you stay out of cloud (which you know you must). That aside as others have said winter flying can be some of the best you can get and during cold spells like the current one the air more often than not is dry and clear.
Enjoy.