Storobia Archive
The name Robot Santa comes simply from their use in both appearances to date of traditional Santa Claus outfits as disguise. Underneath they are fairly traditional humanoid robots with gold faces and black eyes. They are not inherently connected with Father Christmas and certainly appear to have little appreciation of the season of goodwill!
The Santas use Killer Christmas Trees. These can spin at high speed cutting down everything in their path and also launch explosive baubles.
In The Christmas Invasion the robotic santas worked with the Sycorax - it's uncertain whether or not they were actually working for the Sycorax. Here the Doctor referred to them as "pilot fish" seeking out his regeneration energy and guiding in other larger creatures, namely the Sycorax.