At the higher elevations (or even at lower elevations in poor weather) it can get quite nasty. Mt. Shasta is so tall that it creates its own weather. As you ascend the temperature drops, the winds increase, and you slow down. It is not uncommon for the upper elevations to hit near blizzard conditions; sub-freezing temperatures, extreamly high winds, snow, etc. I've seen storms come out of nowhere changing otherwise reasonable conditions to nasty in just minutes. At times like these you can't be too warm.
The best way to deal with these extremes is to bring many layers. Special under layers that help keep mosture away from your body yet still provide a thermal layer are particularly good; this is what the polypropylene or silk underwear is good for. Also, don't forget your head. A balaclava is a great multi-purpose knit hat kind of thing that can be used to really keep your entire head warm.
Mt Shasta Weather Links:
NB: much of this info is for the city of Mt Shasta at the base of the mountain - not at elevation!