Giardia is inactivated at a water temperature of 180° (some sources say 170°, but better to aire on the side of caution), so the water does not need to come to full boil to inactivate the Giardia. The only other effective way to inactivate Giardia in cold water is to filter it, chlorine, Miox, chlorine-dioxide, and iodine become much less effective when the water is around 5°C (about 41°F) than above 20°C (70°F). In summation, if you're not filtering or boiling it, you shouldn't even bother adding any chemicals. Yes, the filters will freeze. However, if you shake them out as much as possible and use a fiber filter that has some elasticity to it, it will thaw out when you use it again. If you use a ceramic filter, you run a significant risk of ruining the filter porosity by the expansion of the water trapped inside.
Something to keep in mind here is that there are lots of diseases that can be picked up other than just Giardia. Many of these cannot be filtered and thus must be disinfected. So, if you're worried about these and not Giardia, then adding the chemicals will help, but you will have to significantly increase the contact time or increase the concentration dosage to compensate. This is called
CT, and is a measure of the concentration of the disinfectant and the time it's exposed to the pathogens.
I'm just relaying the facts as they are relevant to winter hiking. Those who chose to not filter or boil at least look at the water source prior to drinking, which is a good thing, but it's really not an indicator of the water quality. Common sense does matter, but it'll only carry you so far. It's true that many people have been hiking for years without any problems, and I was one of them. But since I have been working in the field, I've realized I was playing Russian Roulette with my drinking water and chose to take steps to minimize the chances of infection.
What everyone does with this information is up to them, I'm not trying to preach one way or the other, I've always thought people should be left to make their own choices. As for me, I'll continue to filter and add a disinfectant...where necessary.
Here is some good information on disinfection and sterilization, to include hand sanitizer and many other useful items of interest.