I mean, you usually have both. Because while lakes freeze over, ice fishing is very much a thing.

Also, streaming water doesn't freeze.

I would say there's sometimes (often, even) a lot more snow than there is water. So idk, do you count snow as ice? I guess technically, because it is ice crystals.

And especially before the industrial revolution, you could just grab a bucketful of snow and put it on the stove if you're too tired to walk to the extra 10 steps to the well. You still don't have to go far into the woods and the snow would probably be more or less edible (it definitely is, but like per regulations idk), but especially before the industrial revolution it would've been ultraclean.

And also if you're taking it from pine branches you'll get a nice piney sort of hint of a taste. (I ate snow from the trees as a kid, just don't eat yellow snow)