I could see saying the handwriting "appears smart". I think there would be better ways to say it though. Like "The handwriting appears to be from an intelligent person". The handwriting its self has no intelligence. This is why I want to make it clear your meaning- it reflects the creator of the writing.

"Writing smartly" could mean to write with good ideas or it could mean to write with good hand-writing style. If you mean the first way: "It is vital to write with a clear purpose and direction. " In the second way. "It is vital to write clearly and legibly." However, these days, handwriting is used less and less, so I think you want the first one.