No. Hosting your own email does not make your email private. OpenSMTPD and OpenBSD do not make your email private.
Host remotely (VPN or dedicated server) OpenSMTPD on OpenBSD. Who can read your email?
-Anyone with physical access to the machine. Even if you use FDE, the disk encryption key is in memory while the machine is running.
-Anyone with administrative access to the machine (in the case of a VPN).
-Law enforcement with a valid warrant or NSL (in jurisdictions where those are even necessary)
-Sufficiently motivated and funded intelligence agencies
Host locally. OpenSMTPD on OpenBSD. First of all, good luck. Most ISPs block port 25. If you have a dynamic IP, it's going to be a pain, too. Plus many email providers will have your IP range blacklisted. You will likely not be able to even get this working reliably. But, let's say you do. Who can read your email?
-Same as above. Some of these categories of threats may be mitigated if you keep the machine under lock-and-key and you're nominally the only one with physical access. But you're still susceptible to a warrant, to crackers, etc.
Now, it gets even more fun from here. Let's say you have a setup like either of the above.
Scenario 1: You send an email to someone whose server doesn't use TLS for SMTP (there are LOTS of these). Your email is in plaintext in transit. The NSA has it. If it has gone international, other intelligence agencies have it. Law enforcement has it if they want it. Whoever admins the server you sent your email to can read it. Any bored network op between you and the server you're sending to can read it.
Scenario 2: You send an email to someone whose server uses TLS, but isn't a major provider. Your email is probably safe in transit from Joe Sixpack the network op. Whether the NSA or other intelligence agencies can get at it depends on how broken the CA system is and whether the private keys for the certificates involved have been compromised at some point. So your email is possibly safe from mass surveillance in transit. But it's sitting in plaintext on the destination server. The server admin can read it. Law enforcement agencies and intelligence agencies can get it if they want. If the remote system is compromised by a cracker, they can get it, too.
Scenario 3: You send an email to someone at Gmail, Yahoo, or Hotmail/Outlook (protip: that's most people). I know Google uses TLS for email now, Yahoo and MS probably do too. Yay. But hundreds of people at those companies can read your email if they want. And the American government now has a copy.
So let's put the "hurr host your own" maymay to bed. There are valid reasons to host your own email, but hosting your email does not make it private. Email was not designed to be private, and any system designed to make email private is hacky and bolted on.
The most widely deployed way to make email private is PGP, which is painful to use (and is, thus, not used widely), does not provide forward security, and does not mitigate the tons of metadata that go along with email.
EMAIL IS NOT PRIVATE.
If you want to communicate privately, use Pond, Ricochet, Signal, Tox, XMPP/OTR, or I2P-Bote.
Or if you're the kind of person who likes to pour hot wax on your genitals and sound your urethra, use PGP and try to persuade others to use it too.