The Frenchman deciding to give Joey back to Albert
In no man's land, the British soldier manages to reach Joey without getting shot. When he realises he has no cutters, a German soldiers comes foward to help. When they realise they need more than one cutters, various German soldiers toss over theirs to help.
And afterwards, when they realise that they have fundamental differences as to who gets the horse, and it looks like it might end up in a fistfights and guns... they toss a coin for it, shakes hands, and leave peacefully.
Albert is forced to auction Joey at the end of the war, as only officers are allowed to keep their horses. He walks out of the stables with Joey... and is met by the entire regiment. All of them have pooled together what they had to raise money for him to buy Joey back. Even the major put some money in, though mum's the word.
Albert saving David, the son of his family's cruel landlord on the battlefield. He had been a real Jerk Ass to him up until this point, making fun of Albert for carrying around drawings of his horse. When he gets injured and Albert drags him to a safe place David looks like he wants to apologize but Albert stops and him and just says "We're both Devon boys."
This becomes even more heartwarming later, when Albert is forced to auction Joey; David, who's an officer, tried to say the horse was his so Albert could keep Joey.