Is it possible to send an encrypted message to an owner of an address using that address's public key?
Potentially possible or possible right now?
Potentially possible, yes of course, check out Bitmessage for an implementation of that.
Possible right now: No. Bitcoin is not designed to even find out where a recipient of a message/transaction is or if an address even has a known private key. Everybody in the network would need to receive your message and check if they have a private key to decrypt it. Also Bitcoin is NOT a messaging system...