Generally speaking your body should not be affected, given that you have normal bedding (what you usually use) and room temperatures at home. Your body is great at maintaining a regular temperature and will adjust to the cold weather!
With Natural Cycles it is important to measure your basal body temperature in your mouth and underneath your tongue. By closing your mouth and breathing through your nose you can avoid external factors like room temperature influencing it. This is why measuring your temperature on your skin or in your ear is not accurate enough to use with the app.
We also want to point out that electric blankets and heating pads can have an effect, so keep an eye on your temperature curve when using these. Winter is also the time of year where a lot of us get sick, so if you feel unwell and your temperatures are much higher than usual be sure to disable the measurement until you feel better again.
Read more about measuring the basal body temperature related articles here: