Can Horizontal Radiation Fluxes Contribute to Net Column Heating?
Yes, there are horizontal radiation fluxes. These can change the heating rate by 10-40 K hr$^{-1}$. They also change depending on the extent of the atmosphere you may be considering. One can also imagine that they are a bit stronger during the sunrise and sunset, when the sun is not directly overhead and the beam has a larger horizontal path length.
There is work, such as the Neighboring Column Approximation which tries to get around that. There's another paper, but I can't find it right now that also tries to resolve this issue.