This will show you one way to build yourself a Ski Bike (aka Snow Bike, Skibob, Skike, or Skicycle). It is a downhill only machine and if you like bikes a lot, then it will probably keep a stupid grin plastered on your face all the way down whatever crazy hills you choose to take it on. It is easier to ride than it looks and is quite stable at high speeds (not sure about the speeds you could achieve at a ski hill, but its worked great for average hills in Wisconsin).
There are many ways you could build one of these, this is just one way to get you started.
Build one! You won't be sorry.
Step 1: Get a bike
Find yourself a bike that you think would be suitable. I like to keep it small so that its easier to kick with your legs or do a running start and hop on. Smaller is also generally lighter and easier to carry up a hill. In addition, if you crash, you're closer to the ground. I got this BMX that someone was just throwing away. (Seriously, it just had a blown tire and slightly crooked front wheel, wtf?)
Strip all the unneeded parts off the bike. Namely, brakes, wheels and chain.
Look for a removable link in your chain to make your life easier. If there is none, then use a chain tool to push out a rivet. Or just chop it, whatever works.