Filter, tablets or boil?
On most trips I carry a small squeeze filter and a strip of chlorine dioxide tablets as a backup. The filter is fast and the water tastes like water; the tablets weigh nothing and do not care about frost.
The filter has two weaknesses. It clogs on silty water, so a bandana as a pre-filter goes in the same bag, and it must not freeze once it has been wet. From October it sleeps in my sleeping bag.
Boiling is the fallback I actually used once, when the filter cracked on the first evening of a two-night trip. It works, it costs fuel, and the morning coffee was late.