that has a spec for "lens filter diameter" will have the screw-mount capability for a screw-on fish-eye lens.
A handle can be added (see "Scorpion" or GlideCam StuntBar - among others).
Shooting snowscapes is no big deal - the auto exposure can deal with it - or you can set it to "outdoors". Pretty much all real camcorders have some sort of control like this.
Start with a budget - let's see what fits.
As for "shaky video"... you will get that with a camcorder, too. To resolve this, stop shooting handheld. Use a tripod or lean against a wall or use some sort of stable surface... when shooting to get non-shaky footage.
My friends and I are into action sports, such as skiing, snowboarding, skating, surfing, and dirt bikes. We've always messed around with cellphone cameras and we have a whole bunch of choppy, shaky footage, but we're looking into getting a decent video camera to film with.
Can anyone offer suggestions / ballpark price-range for the below setup?
Video Camera (preferably HD)
A Fisheye Lens
Some sort of handle/mount
Also, any tips on shooting snowscapes, where there's a lot of reflection and brightness?