The Specifications page in your laptop manual would normally tell you the acceptable operating temperatures your system is rated for. This tends to be down to about 10 degrees Celsius (50F) but can vary depending on exact make and model.
In my personal experience, using a system below rated temperature will usually work, but the display starts going slow, taking longer to display and leaving afterimages. Also, condensation starts to become an issue with near-freezing temperatures. If you notice frost building up on the system, be cautious.
Batteries don't work very good in the cold though. If you do use it below rated operating temperature, you may experience low power problems. Not so much a concern if you're plugged into mains power.
Another related issue, if you're going to be in a mountainous area, is that altitude is also an operating concern with some components (hard drives in particular). Again, this should be listed in the Specifications page, but you're probably fine if you're not going near or above 3000 m (~10000 ft).