Another thought crossed my mind. This is from the really old days. When you do water changes, you raise the level in the tank. If you go above where the glass meets the controller on your heater, and there is a break or crack in the insulation, you may be electrocuting the fish that come too close to the heater. Usually this also is accompanied by eratic swimming behavior by all the occupants of the tank. (it messes with the lateral line).
50 gallons isn't that bad. I live in Montgomery and age my water a week. I use a Rubbermaid Brute 44 gallon trash bin and run the water through floss and carbon. The reason being that the water here is just full of iron and I pull my water before the softener. After a week of running, the floss is a nice dark orange. As of last Sunday I have not noticed any signs of stressed fish after water changes.
On another train of thought, Winter often is accompanied by ruptured water mains. Have you noticed any street work in your area? Even if it was 3 weeks ago any 'bad' water or sediment is probably still in your hot water heater.
What kind of filter - i had problems with canisters going south during the time it takes me to do a water change.
Are you looking to be involved or commited
A Pig and a Chicken are walking down the road. The Chicken says, "Pig, I was thinking we should open a restaurant!". Pig replies, "What would we call it?". The Chicken responds, "How about ham-n-eggs?" The Pig thinks for a moment and says, No thanks. I'd be committed, but you'd only be involved.
I have heard of "aging" water but to keep 50ish gallons (I have several tanks) would be tough. But I have to do something. As I said I've had tanks for years and this is a first, we'll second in as many months.
Personally, i think test kits are way over rated. If a tank is established and you perform regular maintenance, a test kit isn't really necessary.
One thing to consider - when it is very cold, gases in the water react differently. I dont recall if they are more or less dissolved in the water, but the impact can be very detrimental to your fish. I have seen this in various protomelas and placidochromis sp. If possible, let the water stand over night when it is really cold. Just agitate it with an airstone.