Did the Tang poets write love poems?
I am no scholar of Chinese poetry, but my guess is that they are both rare and oblique. Here's one example. Next I'll show you a famous Korean sijo (written 700 years later) as a contrast.
To someone I shall not name after Li Shangyin Draw the curtains in your house to hide our raptures. All night long I hold you in my arms. First the trees are shaken by the storm, then ravished by moonlight. No good can come of our love, and yet my poor heart is joyful nonetheless.
How poignant!