Paint hides wood discoloration and potential rot areas. You bought something with a high maintenance requirement. Those masts should come down at storage time and kept out of the sun. You really don't have a choice. Care for them.
New spars are a little pricey.
On the other hand, every day you see those beautifully finished spars will be happy days. The paint is peeling of in spots on both masts. I have not owned a boat with wooden masts before. Gives you the opportunity to find any soft spots, plus ensures maximum adhesion for whatever you put on. A coat of epoxy sealer is a great base coat.