Here is how you should care for your axes:
Just soak the axe head in BLO every so often and keep the shaft well coated at the same time. BLO does wonders for wood. I personally took a bucket and some PVC pipe and made an axe bath out of it. I just slip the handle down the pipe and the head sits in the bucket then fill it full of BLO (boiled linseed oil) and let it sit for a while. Depending on how you attach the bucket, this little build can last you for years and keeps you from having to rehaft your axes every couple years in really dry places. Even if you don’t go as elaborate as a setup as I have, just put some BLO in a bucket and put the axe head in it to soak every few months as needed.