The low position of the sun in winter makes it a perfect time to shoot silhouettes. You just need to find a bright background (the sky's perfect) and the right subject to give you a shot with series impact.
A compact or DSLR can be used for this technique and a light but sturdy tripod is easier to walk with while still offering maximum stability.
As there's no textures or tones to grab people's attention strong subjects that are instantly recognisable work the best. In winter, wildlife (deer in particular) work well. Even more so if you're shooting on a cold morning when the breath can be seen in the air. The bare, skeletal-like trees that cover our landscape at this time of year also work well as subjects for winter silhouettes. Higher up, turn rolling hill sides into dark shapes that curve across your shot. Fog can help add interest and contrast to the shot and exposing for the lighter, foggy parts of the shot will give you the silhouetted hillsides you're looking for.
You need a bright background for this technique to work and the sky, particularly when there's a colourful sunrise, works particularly well. You can also use a large expanse of water if you live near a lake or the coast too.
To create a silhouette, expose for the brighter background rather than your subject as by doing so your subject will underexpose, appearing very dark if not fully black. Using the spot or centre-weight light measurement modes on your camera should give you the results you're looking for or you can use exposure compensation and select -1 or -2 to deliberately underexpose your shot.
If you're using a compact camera simply point the camera at the brightest part of the scene you're photographing, press the shutter half way down and don't let go of it. Next, re-frame the shot then press the shutter button the rest of the way to take your shot. This should fool the camera into giving you the exposure you want but you may have to try exposing from different parts of the image to create the silhouette you're looking for.
You might want to meter from your background but you don't want this to be your main point of focus. So, to ensure your main subject is sharp, use a smaller aperture to maximise depth of field. You can also try pre focusing your shot before you set your exposure or switch to manual focus. If you're using a compact camera try using Landscape mode as this will let the camera know you want to use a small aperture so your shot has front to back sharpness.
The Sun's Position
Try to position your subject in front of the sun when you're framing up as you should never look through the camera directly at the sun as you can permanently damage your eyes. If you want the sun to be in frame, use the Live View feature so you can frame up safely.
Turn Flash Off
If your flash is set to go off automatically make sure you switch it off otherwise it'll light up your subject and you won't get the silhouette you're looking for.
Don't think you have to fill your frame with your subject as a little space around them will leave room for the brighter, colourful background to show, giving your shot more interest and impact. This is where a wider lens comes in handy as you'll be able to get more of your background in shot. Of course, getting close to a shy animal with a wide-angle lens is easier said than done but you could try putting your camera on a tripod and use a remote release to fire the shutter button. Just remember to focus the camera on a fixed spot before you go into hiding. Having said that, if you're using a long telephoto lens to capture your winter wildlife from a distance you should still have plenty of room around your subject for the lighter background any way.