I have taken the Prius from San Francisco to Lake Tahoe on a couple of occassions, and had no issues at all. Two adults, one baby, and one big dog; plus all the crap for the baby and the dog.
We have also done the SF to Seattle run a couple of times, which includes some pretty high and steep mountains at the CA/OR border. Again no issues.
Never an issue with snow either, but I haven't been in either place when it was bad.
The first trip I took to Tahoe in the Prius, I was actually a little nervous about it. I needn't have been. I never ran out of battery power -- well except when we went to leave Tahoe and as I was loading our luggage into the car and saying our goodbyes I had left the car booted up (it was about 10 days old at the time, so I didn't realize). Sine the engine wasn't "running", I didn't realize it and ran the battery to the red. But that was my fault, not the cars.
In the end, the only way you will know is to try. Your driving style will be different than any of ours, and the exact rate and length of accent will be a big factor.
Spike