Is signing a hash instead of the full data considered secure?
This is secure, and a lot of systems actually do signatures this way (for example, PGP). One reason to do this for performance. Signing a hash is much faster than signing your whole message. It is also non-trivial to hash large messages since signature functions usually operate on a bounded size input.

An attacker will have just as much difficulty forging a signature on the hash as they would forging the signature on the message itself.