Talk about war horses. There was one very nasty war horse in World War one about which a book was written, Bill the Bastard. He would only let one soldier ride him without throwing him off. His heroics though are legendary. Great audible book with a great reading.
I had a great-great uncle who was in the Lincolnshire Yeomanry and he served in Egypt and old Turkish Caliphate, now Isreal. Yeomanry rode horse to battle they were mounted infantry and did not carry sabres. Britain had 64 regiments of yeomanry during WWI. There were usually two or more battalions per regiment while cavalry was organized by squadrons. Regiments were organizational while battalions were fighting units comprised of companies. In a regiment the 1st & 2nd second battalions were regular service battalions, 3rd were volunteers, 4th & 5th reserves.
10/10 would be the 10 Regiment of foot (Lincolnshire Regiment) 10 Battalion (Grimsby). In peace time usually 3 bttn per regiment. In war time as many as 50 bttn per regt. Nominal full strength was 1200 men per battalion, 10 companies. Starting WWI Britain maintained 107 infantry regiments and 5 regiments of foot guards (Grenadiers, Coldstream, Scots, Wlsh, and Irish. Later the Guard Machinegun Regiment, and a Guards Cadet Regt.)