True, and, with sufficient food and water down they can be left for a few days. However, this isn't what you need to hear..... the pigeons need daily, if not more, attention in the freezing weather - someone has to check that the water hasn't frozen. It's not good to leave food down as it attracts rats and, because the birds are elderly I think that they need someone who is familiar with them and their behaviour to watch out for any illness.
Sue