Is it permissible to only run fingers through the hair when performing ghusl (ritual bath) after janabah (state of ritual impurity) for fear of catching a cold, and what is the correct procedure in this case?

If the intention is to thoroughly wet the hair with water while running the fingers through it, then this is what is required for ghusl (ritual bath). As for wiping over the hair without thoroughly wetting it with water, this is only permissible due to an excuse, such as fear of contracting an illness, or its worsening, or delayed recovery. The assessment of this is to be referred to a knowledgeable doctor or personal experience. In such a case, the matter falls under the category of removing hardship and difficulty, as Allah Almighty says: (And He has not placed upon you in religion any difficulty).