Carrier mobility reduction essentially occurs in strong inversion due to velocity saturation effects, i.e. in short channel devices, so depends much more on the length (L) than on W. See e.g. D. Binkley "Tradeoffs and Optimization in Analog CMOS Design", Chap. 2.4.3. Here's a clipping from the text (p. 16) :
"A primary effect is velocity saturation associated with the loss of effective carrier mobility caused by a high tangential or horizontal electric field between the pinched-off drain (again, saturation operation is considered) and source."