During the winter months the sun's low and the sunrise isn't quite as early so you can venture out a little later if you wish. Your local news channel or a quick search online will give you the time of the sun rise. You can just stay in one place, shooting a particular view or scene but taking the time to walk a few steps to find the best angle of your subject is always advised. If you're feeling a little more adventurous plan yourself a route that circles back to where you park your car.
When it comes to kit, a tripod is essential when working with low light levels and pack the wide-angle lens for capturing sweeping shots of the landscape. A longer zoom won't be out of place either, plus pack a range of filters including grads and a polariser. A graduate neutral density filter would be useful in case you find the sky's a lot lighter than the ground. While a polarising filter will reduce glare and deepen blue skies
If you want to shoot wide vistas with foreground detail use your wide angle lens while telephotos let you pull in detail and are also excellent at putting objects within their environmental context.
Morning light can be cool sometimes so try using the cloudy or shade white-balance settings on your camera to give the shot a little more warmth. You'll also need longer exposures and this is where your tripod will be useful as you don't want shake spoiling your shots. It will also slow you down, making you stand back and evaluate the scene in front of you.
While you're out early try capturing a sunrise shot. If the sky was clear the night before there's a good chance you'll be able to capture a cracking sunrise but if a little bit of cloud starts to appear don't worry; it will help diffuse the light. As the sky's bright and the ground's dark your camera may struggle to expose correctly but bracketing can solve this or if you just want to focus on the sun try spot metering. Never look at the sun through the lens, though as there is the risk of eye damage. Instead, make good use of your camera's LiveView feature or just compose with the sun shielded behind something solid.