Can you run the plumbing for a pedestal sink through the floor of a one story home?
Sure. The question is whether or not it will freeze during the
winter. == Answer== are talking about putting the plumbing outside
the inside wall of bathroom? If so i would not do it. all the pipes
showing would look like hell. If you did it under vanity it would
be fine. You would be inside house so do not worry about freezing.
If you did put in a outside wall make sure it is insulated right.
And then hope for the best.