What do Boxer's and Mollie's actions at the Battle of the Cowshed show about them?by actions I mean, what does it show about their character?...

Boxer and Mollie's actions at the Battle of Cowshed represent their opinion and commitment to the rebellion and its aftermath.

Boxer is very committed to the rebellion, he is a hard worker, believes strongly in the ideas of animalism and does not question the authority of those in charge.  He works harder than the other animals, accepting that this is his fate, his contribution to the cause.  Boxer trusts that the social order that is established at Animal Farm will in fact bring about the opportunity for him to retire one day and graze at leisure. 

He remains committed to this belief even when he is hauled away in an ambulance to the glue factory or slaughter house.

Mollie exhibits her lack of interest in the rebellion, the organization of the farm, working on the farm or participating in any activities that are dangerous.  By her absence at the struggle with the humans, Mollie's feelings are clear, she wants her old life back, or some form of it, to be taken care of by a human, to have her mane brushed and fixed with pretty ribbons and to eat her lump sugar.

 In fact it is not long after that Mollie is taken off the farm by another human and is seen pulling a carriage.