Short answer: It is possible, but I wouldn't do it.

How can you do it? Pretty easy, setup the mysql server to accept connections from your home pc. Either by limiting access to a subnet, or if you got to a specific fixed IP. Then just enter the data for the mysql server into your MySQL.conf, and be happy.

Why shouldn't you do that? Two points. One is security. The server needs to be accessible, and your data is running over the web. Even with the encryption on stuff like login information it might be read anyways. And the server itself my be more suspectible to unwanted outside access. Second point is latency. Any connection running over the internet always has a higher round-trip-time then any local connection, or even a connection on the same computer.