As I am currently residing in Indiana, a place that can't seem to stop getting mounds of snow at inopportune times this year, it is only natural that my thoughts are of winter--specifically, how winter can be presented and used in a roleplaying game. Below are a few ways winter can be in the context of a RPG:
Winter is a physical challenge. Think about how cold you are just walking in from the parking lot to work in the morning. Then think about a journey of even 50 miles, on foot or on horseback, near-zero winds cutting into your heavy, suffocating clothing. Think of having to spend the night in the middle of an ice storm, with only the barest shelter. Thinking of never being truly warm for days on end, of losing extremities to frostbite on what modern-day folks would consider just a jaunt down the interstate highway.
There's a reason many armies used to go to winter quarters rather than continue campaigning through the dead of winter. Even simple travel can be frustrating, slow, painful, and even deadly.
You don't need to use frostbite rules and exact gauging of temperatures if characters are out gallivanting in that sort of environment. But you can throw in some reminders that it isn't a walk in the park.
You can also use winter as a physical limiter/inducement--"we have roughly two weeks to force our way through this mountain pass before the snows make it impassable!".
Winter is the continuation of gaming by other means. Games such as Pendragon allow for an offseason for characters. In the winter, instead of crusading or dungeon delving, knights and nobles may go home to manage their estates. Soldiers make camp, drill, and plan for spring's campaigns. Adventuring parties may pack it in and winter in a city near the wilderness they've been exploring all summer, giving the opportunity for some new bad guys, city intrigue, and alley crawling. Whether you decide to concentrate on character growth and training or use winter to change venues, it can be an interesting change-up for your game.
Winter is a theme. From frost giants to elementals of ice, there have been a metric ton of baddies designed for use in frigid climes. Don't be afraid to throw these at your players--note the passing of seasons with seasonal enemies, as it were. This can also help keep things fresh in the bad guy department.
You can also frame conflicts in the contexts of a harsh winter. A goblin raiding party just isn't out for loot and slaves--hunting is poor, and they've taken to raiding villages just to get enough to eat. Towns you pass through may be wary of strangers, frightened that they wish to take from their pitiful food stores that they're hoping will just see them through until spring. In a tough winter, hard bread and mealy carrots can become more valuable than platinum.
Winter is down time. Some groups skip right over winter, and get back to when the adventuring is good. Sometimes, this can coincide with the real-life holidays break. You should never feel forced to include winter challenges if they don't fit the style and tempo of your game, but as you can see from above, there are many reasons to do so.