Red coated Santa was apparently used first in marketing in America. Before that, Santa wore all types of coats, green for instance:

While the Russian Empire was marked in red in some maps from the Romanov times, the Green Color was considered the one in which the Empire ought to be marked in.

Marking Russia in red is inspired by the Soviet flag. Make Russia Green Again. Also build a Pleistocene habitat in Siberia with woolly mammoth. Make Mammoths Shit in Siberia Again.