I too have angular cheilitis that is exacerbated by the cold weather. I suffer from October through to May. It goes from one side of my mouth to the other and each sore will last for weeks. Although it's a good idea to get checked out, I don't think it's always related to poor health. I am very fit and healthy but do run outside in the cold so think that does contribute.
I think I have found a cure - at least for what I have. Back in October, I bought some Tea Tree Oil at a local pharmacy. This is the pure stuff and has a fairly strong smell. Anyway, Tea Tree Oil does have anti-fungal properties. I mixed it up with a little vaseline and applied it to my lips. The sores went away. Now when I feel them coming on, I apply the tea tree oil several times a day. It can be drying but it does the trick. It's now mid-January and I haven't had an outbreak. This is a first in years.