Several people have replied to this, some favouring scrape, others sticking with paw, with the odd mention of scuff or hoof. Many thanks to all who replied. I thought I'd better show you the context of the question.
The night before the Battle of Waterloo was very wet - something that decisively influenced the outcome the next day. Most of the troops had to rest the night in the open. It was a horrible way to spend what would be, for many, their last night on earth. This description of the experience of one cavalry regiment is a fair representation of what was happening all along the Allied line.
The problem with being a Staff officer was that you were denied the right to moan about conditions. All around, he knew, captains and lieutenants were muttering to each other about the imbecility of their commanders. As a member of the Staff, Burke was, in the view of the lesser beings who did not share his privilege, a representative of the very commanders being complained about. He must conduct himself so as to convince the 8th Hussars that any hardships that they might have to endure were completely justified by the military necessities of the situation.
Duvivier beckoned him over. ‘In weather like this, the French cavalry often sleep in the saddle. It spares the riders a night on wet ground, but it tires the horses. I won’t have it in my regiment. Spread the word.’
Burke moved through the column. Most of the men had served under the French and, as Duvivier had anticipated, many of them had no intention of dismounting. Burke could understand their feelings. The bad temper of the men was picked up by their horses: they fidgeted and scraped at the sodden ground, turning the area around them into a quagmire.
‘Captain! Colonel Duvivier requests that you order your men to dismount to rest the horses.’
A dozen times he gave this order to a dozen young officers, who responded with varying degrees of ill humour as their troops cursed Napoleon, the weather, and their colonel but, Burke noticed, not in that order.
The horses were under no orders to rest on the ground and, being intelligent creatures, did not do so. Instead they stood morosely in the rain, tethered to pegs hammered into the mud. The mud, of course, did not provide any real grip on the pegs, so the horses often pulled them clear from the ground and wandered off in search of fodder. Burke decided to take advantage of the liberties that came with his Staff rank and wandered off himself to see if he could find anything for his horse to eat. Once fed, it might not pull out its tether and, if it stayed still, Burke would try the cavalry trick he had seen of sleeping in the shelter of his horse. He had been assured that a well-trained horse never trampled a man lying beneath it and he was desperate enough to get out of the rain to believe the tales of men with more experience of war horses than him. In the event, though, there was no fodder to be found. While the withdrawal had been orderly, it was too much to hope that the provisions would have arrived at the same time as the troops.