Hi Shiloh,
Is it really a *3000* ft climb ? That would put your house at about 80000 ft above sea-level ..
I live in the foothills of mile-high Albuquerque, about 400 ft above the city, so we may have similar topography. My only winter experience with our Priius II was 2004 - 2005, which was pretty mild. The Ford hybrid, and of course the toyota suv hybrids have similar drivetrains, and I would guess would have given similar experiences:
Heat: is better than our Subaru Impreza Outback, because there is no reliance on engiine heat, coming instead from the battery. So the car heats up immediately. This does mean that the ICE will be on more in the beginning of your drive, even if you are going downhill, but not a problem. You may be interested in
www.john1701a.com, a wonderful website from a fellow from MN. Serious winter driving.
Long Climbs: As has been mentioned, the worse scenario is that all the battery has been used up, and the car essentially reverts to a simple ICE drivetrain. I have never seen that happen, even going up the **5000** ft Sandia Mountain in my backyard.
All told, performance is in all likelihhood a non-issue. You may not see EPA mpg, but I'd expect your mileage to be markedly better than a conventional suv, and emissions are SULEV. Colorado has one of the nations most generous state credits for hybrid purchases -- somewhere around $3K. I'm kind of surprised anything else sells there.