Is it secure to transmit a short plaintext with its MAC?
A normal security notion for MAC's is that of unforgeability. So given some set of message,tag pairs $(m_0,t_0),\ldots,(m_k,t_k)$ is should be hard to create a tag for a new message not among the $\{m_0,\ldots,m_k\}$, stated informally. 

In your case, you could just use $E_k(m_0)$ with the secret MAC key $k$ ($H_0$ in your notation); no need for the extra XOR (it does nothing for security; you know $m_0$ anyway, so we might as well use $E_k(m_0)$). This is just a standard use of a keyed random function (which we will suppose a block cipher is) as a MAC for short messages. It's construction 4.5 on page 117 in Katz and Lindell (second edition) book "an introduction to modern cryptography", which also has the (short) security proof for this construction for the above notion of security.

You do realise that your construction does allow for replay attacks, I suppose?