If your pup is having dry skin itching it might be either due to a fungal or bacterial infection. We would suggest the following:
1. Check for any tick and flea infestation.
2. If not tick and flea, check for indications of rashes or redness on the skin.
If you find rashes or redness, connect with a veterinarian immediately. Based on the nature and extent of the rashes the vet may suggest medication to counter the infection. Hair fall is often associated with change of weather. However, if your pup is having a skin infection, the tendency of the hair fall will increase.
Please connect with a veterinarian for medication and remedy.
We wish your pup a speedy recovery.