Anthony Lakes Ski Area
Some of the most powdery ski conditions in oregon and is just 35 miles from baker city. (http://www.anthonylakes.com/)
The Hells Canyon Scenic Highway
This is the southern end of the hells canyon scenic highway which follows rte 86 east of town to the snake river on the oregon-idaho border. the scenic drive can be followed as a big loop around to joseph and la grande further to the north. be aware that driving the entire loop may not be possible during winter as some roads are not maintained and can be blocked by snow. this situation may exist well into spring ie: late april. some of the roads traverse high terrain where winter snows may linger longer than you might expect.
The Elkhorn Scenic Byway
A wonderful drive through the elkhorn mountains just outside of baker city. it follows highway 7 to sumpter and around to haines past anthony lakes ski area and the north fork john day river wilderness. this route is also often tough in winter. (http://www.byways.org/exp...)