Can my car handle the mountains?

So I'm about to move to Lake Arrowhead ca from LA, but I'm a bit worried that my car wouldn't be able to handle the driving there. I drive a 1964 ford mustang that is in really good condition, but my realtor said there's no way I should be driving it up there especially since I'll be making an almost 2 hour commute to college every other day. I haven't driven up there yet with it but I've been a countless amount of other times on vacation and it is a very big hill to get up to where I live. I also know that it snows up there, and can my car be driven in the snow? Is this hopeless or do I have to buy a new car? Answers appreciated.

The first thing that came to my mind was, what did they do back in the 60's when this car was produced, I'm sure those mountains were there at that time.
I guess if it's in really good condition like you said, and if you put snow tires on it all around, it may work, It did back then, why not now,
I guess it would also depend on how much snow you got too.
If you have to buy a car, buy a used Honda Fit, good on gas, and fun to drive.

It all depends on the condition of the motor and how old it is. If it is the original motor, then you might want to consider getting something a bit newer. And a rear wheel drive car like that is the worst possibale car to have when it is snowing. So yeah looks like a newer car is in your future.

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