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.