I have a chair that came with my serger. It has a deep storage space inside to store the serger. I have been rolling in that thing for thirty years on carpeting. Not shag rug, but not very smooth either. I just go from the sewing machine to the serger, and surprisingly, the carpet doesn't even show wear where I always roll on it.
My son made a rolling chair for me from a quite grand dining chair he bought at a yard sale. That thing rolls easily on my hardwood floor in the living room. I haven't tried it yet on the carpet.