The water quality in the stream is dependent upon the geology upstream of you. If the geology is largely igneous rock, then the water might not be very mineralized at all. But if the geology is sedimentary rock or largely soil, then the water has a higher likelihood of mineralization.
If the water has only flowed a few (or tens) miles, then its also unlikely to have picked up much mineralization. Go for it.
What are you, a geologist or sump'n?! I am, and you're dead on! Geology has a lot to do with it. I live in California's Sierra Nevada mountains which are all granite, ie. silicate minerals; and my water comes from a water company whose source is higher up in the mountains and is largely snowpack. Based on their annual water quality report, their water (my tap water) is very soft (low in minerals/ions). Much of Europe, where good beer comes from, sits on limestone. I don't know, but I would expect their natural water to be fairly hard, ie. lots of Ca and Mg ions. I also don't know if they treat their water in any way before brewing. They probably didn't hundreds of years ago. As a rookie brewer, I've just started asking these questions myself, which is how I found this thread.
Here's more interesting geology (to me anyway): Coor's "Pure Rocky Mountain Spring Water" comes from the Rockies, obviously, which are sedimentary, and therefore have lots of limestone. Budweiser comes from St. Louis, originally, which also sits on limestone, and is right next to the Mississippi River ("Too thick to drink, too thin to plow"). Bud also has a brewery close to me, in Fairfield, CA, which sits on valley sediments and coastal silicate bedrock, and doesn't have any significant limestone anywhere near it.
All that said, it sounds to me like soft water is preferred by folks on HBT and hard water isn't. I'd be curious to know what they use in Bavaria, which is all limestone. I'm sure all this trivia didn't help anyone decide what to brew with, but your idea, Beerbeque, to brew with mountain spring water sounds like a good one. Benbradford's mention of mining or other contamination is obviously something to watch out for. My beers taste pretty good with my mountain stream-sourced tap water. So which mountains do you live near anyway?