Lewis structure of dinitrogen trioxide
What really happens in nature has higher priority than our believe what happens or should happen. See Dinitrogen_trioxide with the structure, bond lengths and angles.
Be aware both $\ce{NO}$ and $\ce{NO2}$ are radicals with an unpaired electron.
$\ce{N2O3}$ being( $\ce{ON-NO2}$ ) as 2 paired radicals is the direct analogy
to the dimer $\ce{N2O4}$ being $\ce{O2N-NO2}$, both being formed at low temperatures.