I used my psp at Okemo like two weeks ago, it did the job fine, and I fell a bunch and didnt bust it up. just make sure you use the "hold" button and set the screen tot turn off after 30 seconds, my battery lasted more than 5 hours and I got tired of my playlist before it ran out.
Also if you havent yet, get down with modding that bitch. pspmod.com
mpd might be right about ipods holding up in cold, my battery dies practically instantly if my ipod isn't within 1 layer of my body. i would say an mp3 player is good to get for boarding because they're light. cheap ones basically work the same as expensive ones they just don't have as much memory... it's not like you're gonna listen to a week's worth of music without stopping for enough time to put different songs on.