I've been told when doing cardio to breath in through the nose and out through the mouth. Where I live though, the air is cold enough 3-4 months of the year so that deep breathing through my nose stings my nasal passages.
Is this healthy? Should I change up my breathing pattern, or will the stinging go away?
Nose has natural air filters for all sorts of things; temperature regulating filters for example. Nasal breathing is very important at cold weather.
However, there is a lot of debate concerning the general advice to breath through the nose during cardio workouts. You need a lot of oxygen and maybe nose is too small to deliver enough. Many runners breath both through nose and mouth at the same time.
(I should add some sources later - please edit if anyone has some handy)
I recall learning that breathing in through the nose actually warms up the air you breath before it reaches your lungs, more so than when you breathe through your mouth. This in turn keeps your body temperature better regulated.
You could try to exercise when it's warmest outside. However, as long as the air is cold, I don't believe the stinging sensation will go away from your nasal passages.
I find that it is better to go much easier during very cold or very hot weather as my bronchial passages have a tendency to get so inflamed that it resembles asthma. Stinging is a sign that your nasal passages don't like what is going on. Perhaps during winter months you might consider spending time on a treadmill at the gym. In my case, the total lack of humidity is another problem, and major exertion during winter months (which have lower humidity than is normal for Denver) tend to give me nose bleeds.
I personally wear a ski mask, or wrap a scarf around my face, and I breathe through that for as long as I can. Eventually, after about an hour or so, enough moisture will have built up (and, if it's cold enough, this moisture has started freezing) that I have to lower the mask, but that's usually enough for me. The worse problem I have is dealing with my glasses fogging up from the exhaled heat and moisture trapped in the mask.