i am a pti in the army and i do this sort of stuff all the time, running is ok but it is the one you can make so many excuses not to do

swimming is the best if you can do it with any grace and distance

taking a long walk is just as good as a run and less damaging especially if you got some hills

unless your training for something specific then cyclin i find is very good for heart lungs and stamina, not so boring and so many diffo types to do

as for in the winter it's worse your right it's the cold air and moisture on your lung alvi