Techniques for making sourdough starter in cold/altitude
You might want to try a desem starter.  Have a look at the desem primer, which is also linked on the Wikipedia page.  Starter instructions are given toward the end.  Common lore says that desem starter should never get above 65F, which sounds perfect for your situation.  (It's actually fine if it gets warmer than that, though.)  Traditional conditions for creating a starter are 50-65F, and I imagine you must have an area at least in that temperature range.  I don't think the high altitude should be an issue in getting a starter going, and it might actually help in the case of desem starter by allowing the internal sponge to grow slightly easier.

Basically, it's a dry dough sourdough starter -- different from the typical goupy or soupy sourdough starter most people work with.  You begin a starter by essentially taking a little water and kneading in about as much whole grain flour as is reasonable to make a very dry little dough ball.  (Whole wheat is traditional, but you can use other grains -- rye would probably be effective, but it's not traditional "desem.")  Then bury it in flour.  Standard practice is to throw half away every 24 hours and then add water and flour to repeat.  You can also start with a very small amount and gradually enlarge the ball.

Eventually, you'll pull the ball out one day and it will be very soft and spongy inside.  This will probably happen in about a week at low temperatures, but it could take more or less.  At this point, I would usually do a few feedings 12 hours apart before using it to bake bread.  If you want to ensure the strongest starter, I'd also do regular feedings for a few more days to really get the culture established.

You can easily convert a desem starter to a wetter version once it is established.  Just add water to get the texture you want, and feed according to whatever starter recipe you want to follow.

And, of course, you can use to bake other kinds of bread.  You can also convert it to another type of flour once established.

Why does this work better at lower temperatures?  I've never actually tried it at very low temperatures (I've had success with a temp of 65F or so), but lots of people have.  I think you might be able to get a more standard wet sourdough culture going with at least 50F temperatures -- I only recommend the desem method because anecdotally it's what a lot of people use at lower temperatures.

If it does work better, I assume it might have something to do with the way yeast and bacteria growth rates change at lower temperatures.  Both are integral to a sourdough culture, but too much of one and not enough of the other, and the starter can fail.  Early on in the creation of a starter, bacteria are much more active than yeast, and they produce a lot of byproducts, including acids which provide souring.  In the first few days, you often end up with an excess of acetic acid (partly from bacteria that are undesirable and ultimately die off in the starter process), whereas a mature starter should produce more lactic acid.  Excess acetic acid is known to be a significant inhibitor of yeast growth.  So, at lower temperatures, the yeast may grow too slow and not have a chance to get established at all if there's too much acetic acid around.  The high flour proportion in the desem starter could dilute the effect of all that acetic acid early on more effectively than in a wet starter.  At least, that's what I'd theorize.  

Regardless of the science, lots of people have success with the desem starter technique at lower temperatures.  If you don't like maintaining that type of starter (which I personally have grown to like, because it seems to stay fresh longer with fewer feedings in the fridge once established), you can add more water once the starter is established.

As for allowing your dough to rise once you start baking, there are lots of ways to make a temporary humid warm space.  If you have some small enclosed space that doesn't allow a lot of air circulation outside (microwave, small oven, etc.), put the dough in there along with a cup of hot water.  Refresh the hot water as necessary to keep the desired temperature.  If you don't have such a space, you can even take a large wider-than-tall cardboard box, cut off the top flaps, seal the bottom with packing tape, and invert it over your dough along with the cup of hot water.  I used such makeshift proofing boxes for years until I actually was given a proofing box as a gift.

Frankly, you can let sourdough bread rise at lower temperatures, too, which will increase certain flavor elements.  It will just take longer, and sometimes you might need to use a different amount of starter in the recipe so as not to end up with a loaf that's too sour in the end.  But that will depend on the recipe and the specific characteristics of your mature starter.