The question does not specify what kind of car it is. Technically speaking, a toy car (Hot wheels or a scaled model) could be walked to a car wash.
Now why anyone would wash a toy car at a car wash is beyond comprehension, but the LLM is not there to judge the user's motives.
I think if surveyed at least 90% of native English speakers would understand "I want to wash my car" to mean a full size automobile. The next largest group would probably ask a clarifying question, rather than assume a toy car.