Matt, 26, and new sidekick Karen Gillan, 21, were busy filming on location in Cardiff despite the Welsh capital being covered by a white blanket.
A show insider said: "A bit of snow might stop mere humans but not the Doctor.
"Filming is on a tight schedule and has to keep on going regardless of the weather. Doctor Who can work around anything."
Smith is the eleventh BBC time lord and was filming a scene based in present day in Cardiff Bay.
Smith, who has taken over from David Tennant, was on location with flame-haired assistant Karen Gillan who play new sidekick Amy Pond.