P+S cameras can be a little hard to work with, especially concerning exposure. All of your photos have exposure issues and most of them make at least one basic mistake of composition. Straighten the horizons, too.
#1 - The background itself is interesting, but you centered the subject of your image. If you're not familiar, read up on the rule of thirds -- basically never put your subject smack-dab in the middle of a picture. Your exposure on this picture is off too. Obviously that can't necessarily be helped because of your camera, but any interesting details on the leaf are washed out.
#2 - You have nothing that draws my eye into the picture. If your aim was to focus on the icicle, then this picture also has a centered subject. The wall creates a weird divider in your image and the background (snow) doesn't isolate your subject at all.
#3 - I like it. You could probably tweak the exposure a little bit and I would have used a smaller aperture to bring the house into focus as well. The puddle provides interesting foreground and you've nicely put the horizon towards the top of the frame.
#4 - I see what you were going for, but again this picture lacks a subject that draws my eye in. At first, all I see is an amorphous blue mass. It takes me a second to realize it's a car. The car divides your picture almost exactly in half, which is something you want to avoid. Take a look at stock car art, especially the more abstract stuff, to see how the photographers use a single element (grille piece, tail light) as the subject and build a photo around it.
#5 - This one is a fairly solid composition. You have the snow more the 2/3 the way up, creating a nice horizon, and you've got a pretty nice foreground. Unfortunately, your subject isn't terribly interesting and any interesting details are lost because of the exposure issues. You did place it in the center of the frame again (tempting, I know!), so next time, try to move it off to the side slightly. I really like the foreground in this shot and, with something else as the subject, this could be a really good photo.
Snow can be incredibly hard to shoot on / with because it reflects SO much light and I think your camera was having a tough time deciding what to do. In general, I'd recommend underexposing your pictures. Underexposure means that you can generally get the details back in post-processing, whereas over-exposure leaves you with blown-out highlights that cannot be recovered.
#6 - I like this image, though I think it lacks a clearly defined subject. Though there is the open space leading into the image, there is something that doesn't draw me in as much as it should. The shadows are very nice and you did a great job of including the sky, but not too much of it. The wavy line created by the trees is great too.
Keep at it man! Photography can be overwhelming at first, but just remember that everyone started somewhere and that the more pictures you take the better you will become.
IMO, go get yourself a cheaper SLR camera. Though the tools do not make the artist, an SLR will teach you much more than your P+S and it will let you control the exposure. I know you can get a D40 kit for the mid $400s right now, think about picking one up! I would also encourage you to join Fredmiranda or another photography forum. Every day they have people posting images for critiques, which is great for any photographer. You can look at the pictures and understand the compositional elements and you can also look at the comments and start to learn what does and doesn't work in the photo world.