Simple scenario, an airplane with landing gear retracted (less drag) vs the same airplane with landing gear extended (more drag).
Are the stall speeds different on each case?
By and large no. Sometimes there can be a slight interference effect from things like the landing gear doors and the flaps.
However, this is not due to the drag, it is due to other aerodynamic effects.
When landing, you generally want drag -- it helps a clean aircraft descend in a controlled manner.
When taking off, you don't want drag -- you want to be clean to accelerate and climb as quickly as possible.
For this reason, you usually only use partial flaps on takeoff -- enough to improve lift, but with minimal drag increase. You also try to clean up (raise the gear) promptly after liftoff.
However, on landing, you go to maximum flaps -- a little bit more lift, but a bunch more drag. You also put the gear down nice and early, so you can verify that they're down and locked -- and so you can stabilize your approach with the drag already out there.
Edit:
Stall speed is a function of the maximum lift coefficient of the wing / airplane.
$V_\mathrm{stall}=\sqrt{\frac{2\,W}{\rho\,S\,C_{L,\mathrm{max}}}}$
So, things that change $C_{L,\mathrm{max}}$ will change stall speed -- primarily, this means high lift devices -- flaps, slats, spoilers.
A wing that is covered with ice will likely have degraded $C_{L,\mathrm{max}}$.
On a variable-sweep aircraft, it would also mean the wing sweep angle. You might also track a change in wing area with variable sweep.
On a blown-wing aircraft (like the C-17), it can also change with throttle setting. Paradoxically, with a blown wing, you need to keep throttle up to have maximum lift -- this makes landing a challenge. In fact, it is a great reason to have air brakes of some sort.
Anything that affects just parasite drag -- without changing the lifting capability of the wing -- will not change stall speed. So, landing gear, speed brakes, stores on the wings, an open door or window, installing an antenna or sensor, etc.