Pretty much what the question states, is SpaceX doing early work on that aspect of Mars' colonization or are they at the moment giving full focus to the launch system, craft and lander? (which would make sense of course, just curious)
This is an interesting behavior on SpaceX's part.
They are very vocal about near term development, showing off hardware early, building excitement.
Longer term, the booster (BFR - Big F-ing Rocket), its engine (Raptor), and the transit vehicle (MCT - Mars Colonial Transporter) have been named, hints given, but not much more. Well Raptor at least we know its propellants (Methane/LOX), its vague thrust range (Currently around 1 mlbs, but that has changed numerous times), and where they plan to test it (Stennis test stand being modified for Methane ops).
We do not know how big (width of the core, number of Raptor engines) that will be on the BFR, nor much of anything about MCT.
This is the horse before the cart. Need the engine to get there. Planning for actual logistics on the surface, is even farther out.
I have little doubt there is a small team working on ideas and concepts, or even just reviewing the literature for the best ideas to liberate. (Steal one sentence of text from someone else, it is plagarism. Steal 100 ideas from 100 other places and it is called research). But there has been little to nothing said.
I recall hearing Elon mention (but cannot find the reference) that he hopes other companies will spring up, once he has serious work done on BFR/MCT and the likelyhood or a Mars colony is real, to work on Mars colonial logistics.
Elon Musk seems to have a long term plan. His other main investments, except for the obvious rocket launchers and spacecrafts (SpaceX), are in solar power, battery technology and electric vehicles (SolarCity and Tesla). All of that, and maybe some hyperloop tech, would be very useful on Mars. If you look at it in terms of laying the base for key Martian technologies to arrive in a decade or two, I think you can say that he is seriously preparing for a colony on Mars.
Performing even single flight to Mars needs research capacity that single company of SpaceX size have not.
The absence of simple illustrated concept however beyond names is really strange. During the years, a number of concepts of Mars transportation and Martian base/colony have been published sometimes by small nonprofit groups.
For the moment, Mars looks to be rather motivation mantra than specific goal for SpaceX.