If I recall, most of the past mining in SW Colorado was for gold and silver (or uranium). As you are aware, the issue with water from such mine tailings is its content of dissolved minerals, heavy metals and ionic constituents. Around here, (SE Arizona) water leaching through copper and gold mine tailings carries concentrations of mercury, molybdenum, manganese, zinc, arsenic, selenium, copper, sulfate and nitrate all in concentrations exceeding the EPA drinking water health guidelines. Most hard-rock gold, silver and copper mine tailings in the West have similar characteristics; they are acidic and heavy metal rich. Filters and tablets will not remove these contaminates from water; you need a resin exchange column or equivalent for the job.

The clarity of water and the age of the tailings is not a reliable guide to the quality of water, only chemical analysis can identify water contaminated by dissolved minerals.

Another issue you need to consider is that piles of material that appear to be mine tailings may be leftovers from gold recovery using the cyanide leach process.You are not likely to encounter such piles but water from them can kill you quickly and the leach piles are not always identified as such.

Water quality of most of the streams in SW Colorado is probably OK with respect to minerals (but not necessarily biologicals) however you should rely on local knowledge to identify the streams that are not safe. The state may have a register of contaminated streams that might help if you can locate it and access it.

But, to re-answer your original question: no, filters and purification tablets will not make water contaminated with toxic dissolved minerals safe to drink.