Seems to be one of those things that gets talked about a lot, but PPlers have little first hand experience. I am not suggesting that is a bad thing, but if you get the chance when you have got some hours and experience under your belt go find a pilot with even more expereince, find the right day and go see what a little light icing is like, safely.
I personally found the most interesting part the instance with which the screen completely frosted over and equally on dropping below the freezing level how quickly again it cleared.
More specifically with regard to your question, of course the last thing there should be any risk of during your x country is running into icing - it probably means you will be flying on instruments anyway which you are not rated to do, other than a 180 and get away from it quickly.
In short, simply do not fly into cloud or rain showers if you are above or near the freezing level and do not fly into cloud or rain showers on your cross country in any event.