I didn't know there were any electrically charged massless particles.
It is interesting to contemplate an electric charge moving through space at light speed.
I guess it would be able to gain or loose energy on the fly.
According to the Standard Model, a field of the necessary kind (the Higgs field) exists throughout space and breaks certain symmetry laws of the electroweak interaction. Via the Higgs mechanism, this field causes the gauge bosons of the weak force to be massive at all temperatures below an extreme high value. When the weak force bosons acquire mass, this affects their range, which becomes very small. Furthermore, it was later realised that the same field would also explain, in a different way, why other fundamental constituents of matter (including electrons and quarks) have mass.
The electric field for massless QED is very different from what you're used to. Specifically, the electric charge will go to zero logarithmically at long distances, so you won't have long-range Coulomb forces. The heuristic behind this is that it becomes "cheap" to create virtual massless particle-antiparticle pairs which screen any charge. Then it takes arbitrarily little energy to add another particle-antiparticle pair.