Deleted Contacts on WhatsApp but Chat not deleted
Not being able to see someone's profile picture does not mean they deleted you from their contacts. It's possible they simply removed the picture and no one can see it including you.
If the person still has the chat saved, then yes they will see your profile picture.
If you don't want someone to see your profile picture you can delete their contact, and in WhatsApp settings select that only your contacts can see your picture. Alternatively you can block that person's number and they won't be able to check your profile picture