Hmmmmmm.  Welcome to the site. 

Hopefully you will check back in, and someone will answer you.

Drop me an email and I'll share with you what I've got.  It may not be what you're looking for, but on the other hand, it just might be.  It's a Sony Handycam video Hi8 with a 48 power digital zoom and steady shot.  I just put a brand new battery in it last week.  This unit has just about everything.  Check it out on the web to see what you think.  But no matter what you end up getting, have fun filming the boys as they shoot some monster bucks.

elk66@comcast.net

I'll send ya pictures and we can talk about it.

You're going to want somethng that can take a drop, getting wet and still able to work in very cold weather.

You're also going to want something that will record in HD, so that if you need to go back with a PC and edit the footage and use a crop function to zoom in on that whitetail 200 yards away that your boys about to take a shoot at doesnt get recorded as a bunch of fuzzy blocks or static in lower light situations.  Zoom is a handy way to fix that issue without a PC but higher zoom camcorders tend to be up there in the price ranges, and shooting at high zoom without a tripod or even more expensive image stabilization features usually results in shaky, disappointing footage.

My suggestion that seems to fit all of the above criteria, would be the "GoPro" line of cameras

http://gopro.com/

They come with several options.  They are all highly vibration, water and cold resistant.   They have a reasonably large image sensor (better low light picture) and ive even seen them actually mounted to deer rifles with great results.