Assuming this is a loss for the customer, what can she/he do?
While the cancellation of the original flight was due to weather directly affecting the operation of the flight concerned, and you correctly surmise that compensation is not due in this circumstance, there are other provisions that the airline may be in breach of.
Right to reimbursement or re-routing
- Where reference is made to this Article, passengers shall be offered the choice between:
(a) - reimbursement within seven days, by the means provided for in Article 7(3), of the full cost of the ticket at the price at which it was bought, for the part or parts of the journey not made, and for the part or parts already made if the flight is no longer serving any purpose in relation to the passenger's original travel plan, together with, when relevant,
- a return flight to the first point of departure, at the earliest opportunity;
(b) re-routing, under comparable transport conditions, to their final destination at the earliest opportunity; or
(c) re-routing, under comparable transport conditions, to their final destination at a later date at the passenger's convenience, subject to availability of seats.
Article 8, Section 1 - Regulation (EC) No 261/2004
This is the section which concerns the issue at hand.
Your example given includes the passenger being delayed to the next day, even though free seats existed on a flight the same day as the cancellation.
This would, in my mind, be a violation of the wording of choice (c) in the above quotation:
(b) re-routing, under comparable transport conditions, to their final destination at the earliest opportunity;
So, what can you do?
You cannot claim compensation in this example - the airline would probably be able to defend themselves under the "adverse weather conditions" for the cancellation as it directly affected the flight concerned.
However, compensation is not due if the carrier can prove that the cancellation is caused by extraordinary circumstances which could not have been avoided even if all reasonable measures had been taken.
EU Air Passenger Rights Guidance
You can however complain to the airline that they were in breach of Article 8, Section 1 if you have suspicion that the same day flight had open seats and was available for booking.
This isn't a simple complaint however, and the airline is likely to ignore it to the best of their ability.
Therefore, under the scope of the EU261/2004 Article 16 you have the right to register a complaint with the body designated by the member state for the airline and the airport (so, possibly multiple bodies to complain to) that the airline is in breach of the regulation.
Each Member State shall designate a body responsible for the enforcement of this Regulation as regards flights from airports situated on its territory and flights from a third country to such airports. Where appropriate, this body shall take the measures necessary to ensure that the rights of passengers are respected. The Member States shall inform the Commission of the body that has been designated in accordance with this paragraph.
Without prejudice to Article 12, each passenger may complain to any body designated under paragraph 1, or to any other competent body designated by a Member State, about an alleged infringement of this Regulation at any airport situated on the territory of a Member State or concerning any flight from a third country to an airport situated on that territory.
The sanctions laid down by Member States for infringements of this Regulation shall be effective, proportionate and dissuasive.
The EU supply a list of designated bodies.