There are so many things that could have caused the illness in your birds.
Almost assuredly it wasn't cold weather unless you had them heated in the coop and suddenly removed the heat. Chickens are very cold hardy. However, they do not do well if they go from overly heated to cold and back again.
I agree that it could be illness brought on by cold stress, and at the 14 weeks of age, Marek's leaps to mind.
However, Marek's generally doesn't produce sniffling. That indicates more of a viral or bacterial or even fungal cause.
Marek's can remain in the flock and property for years. However, it is believed to be so prevalent that almost all backyard flocks are exposed. The industry recommends vaccinations in chicks, but it is also recognizing the best course of action is to breed from Marek resistant flock...ie the others in the flock who never showed symptoms...so getting rid of your healthy birds is not the wisest course of action. They are the ones that can survive and thrive on your property if Marek's were to be involved (which I doubt due to the respiratory symptoms).
Mycoplasma Gallesepticum (MG) is a bacterial infection that can be latent until environmental stress brings symptoms. It does spread to the flock. How quickly and thoroughly is debated. It generally produces milder respiratory symptoms in chickens with few deaths. It is controlled by antibiotics such as Tylan, however, only controlled as the bird becomes a lifelong carrier. It acts more like chicken asthma. MG can remain on the property for long periods of time, and owners are advised to keep a closed flock...birds coming in who show resistance...no birds going out to others.
Infectious Bronchitis can be virulent producing sneezing and coughing and spreading quickly within the flock. If it is particularly virulent, it will attack the kidneys and you can see death within 24 hours. However, many birds only have a mild infection and once over it are over it. It takes awhile for the virus to clear the area. Some say up to 12 months. Removing litter and cleaning the coop go a long way to rid your property of the disease. I personally had IB in the flock one season. I cleaned the coop/run and kept those who thrived. Happy healthy flock with no further incidence of IB.
Avian Influenza is a grave concern to the poultry industry, and backyard flocks can act as vectors to commercial farms. If you suspect AI, you are to report it to the state ag department. Its symptoms can be sudden death of many flock members. Usually facial/sinus swelling is present, but not always. It is highly advisable to have necropsy done if you suspect AI.
Other than Avian Influenza (and MG which can be passed to new flocks), there isn't too much your flock could catch that would be of great concern to others including yourself. Almost all avian disease is species specific, so you won't catch it from the birds directly or eating the meat or eggs.
That doesn't mean I recommend eating ill birds or eggs from ill birds as opportunistic bacteria frequently grow in a sick bird, such as eColi, Salmonella and Pasturella, Those are concern to humans.
I personally would not rush to cull the remaining birds unless you KNOW that you have an incurable disease that will be forever infecting any future flock. I would take time to try to figure out what may have caused your birds' demise so that you can prepare any new flock better.
Check for mold in the food. Aspergillis can cause respiratory illness and death.
Check for poor ventilation. It is interesting that your birds improved upon bringing them into the house where the air was likely better. Ammonia build up in the coop can do a lot of harm. Do you have your coop too tight for winter? Birds generate a lot of moisture and "fumes" that need to be vented by openings above their heads at roost time.
Are there possible toxins in the area?
So you see, bacterial or viral infection is only one possibility in a host of a number of things.
If you lose another bird, do try to take it in for a necropsy. Some state ag departments will do it fairly cheaply. That way you will know if you've got something that is a long term concern or if some simple fixes can alleviate the problems.
My thoughts.
Lofmc