You'll be fine. It will be rich and down on power, but you will have no problem as long as it is tuned up ok beforehand. The first winter after I got my truck, I decided to hunt the White River area over by Maupin during the General season and pulled my ~3500lb tent trailer over there from Salem. This was with a 350 that had been sitting for 11 years or so and was not in good shape. I had no problem pulling through Government Camp at 45mph plus.
Just make sure you have it tuned right at sea level, lean of peak idle and slightly rich cruise and full throttle will keep you in a totally OK range even at altitude. You'll be down quite a bit of power though. General rule of thumb even for fuel injected engines that are at the right A/F mixture even at altitude is a 3% reduction in HP for every 1,000ft of elevation without forced induction. That means you will be down AT LEAST 15-20% at full throttle, not taking into account loss of power due to it being rich.
A healthy 350 or larger will have plenty of extra ponies available so that you won't really notice unless you are hauling a load. A suped up 350 or larger will have plenty of extra power to not even notice the drop.