In addition to the use of watches, I have seen in many documents, soldiers judging time by the passage of the sun.

Here are some examples:

10 22 1862 [Wednesday]

At six this morning we left the Ford and marched to Powels River, getting there an hour [by] sun.

12 27 1862 [Saturday]

“At daylight we came to Tensaw wharf [north shore of Mobile Bay] and took the boat, leaving this point about twelve o’clock. About an hour by sun we arrived at Mobile. All were interested upon our arrival to see such a number of boats, forts, blockades, etc.”

05 17 1863 [Sunday]

At two o’clock we arose, marched a mile, took breakfast and a good rest and started again for Bovina. At eight o’clock heavy firing commenced at the bridge across the Big Black River on the Jackson and Vicksburg railroad. It resulted into a hot contest, so much so that our forces had to fall back with considerable loss in Vaughn’s Brigade. This done, we had no other alternative but to take the nearest road to Vicksburg and get inside our fortifications, which we did an hour by the sun

11 20 1863 [Friday]

About one hour by sun our Cavalry was driven in [by] the Yanks who followed them to the edge of the town and captured some of our boys. But as soon as they came in range of our guns one piece opened up on them, checking their advance. About sunset the Yanks dismounted and formed their line as though they were going to charge our Battery.

09 03 1864 [Saturday]

We then moved to the left around the west side of town to the north side, so as to connect with other of the command who might gather there and by half an hour by sun most of our force was . . . . . . .The Wartime Diary of John Weatherred, Bennett's Regiment or 9th Tennessee Cavalry, John Hunt Morgan's Command

It would seem to me that these men had spent the greater majority of their time working out of doors and were used to
judging time by the sun's position.