Male, travelling missionaries in the Southwestern States Mission trimmed or removed facial hair as part of weekly grooming and hygiene routines. Moustaches were relatively common but Van Dykes and full beards much less so. In the diaries I detect no “freighting” of facial hair with cultural or religious significance beyond middle-class respectability.
All six male travelling Elders mention shaving, but sometimes the diaries go months between recorded shaves or trims.  Assuming the missionaries were not recording instead of not shaving suggests a shaving frequency of once or twice per week. 
The Elders recorded more shaves in the winter than in the summer  and more on Wednesdays and Saturdays than other days.  They were more likely to shave in the morning than in the afternoon or evening.  In small minorities, shaves were coincident with baths and/or haircuts and other maintenance tasks like letter-writing. 
Elders shaved in a variety of places, most of them buildings, though it was not rare to “Slip in the timber and have a Shave.”  It was also not unusual to shave during the day as part of their missionary visits rather than at the house where they slept.  Shaving was part of the preparation for events like Christmas, the Sabbath, the fair, and leaving the mission.  Companions often shaved each other; using a barber was rare. 
A circular letter from the Northern States Mission a few years prior to the period of this study names the grooming of facial hair as a component of a missionary’s success:
“Special regard should be paid to dress and appearance. Your success largely depends upon the impression you make when first meeting the people; if shabby and unkempt in appearance, the impression you make will be unfavorable. The wise Elder will always keep his…face cleanly shaven at least twice a week (never wearing a big Cossack beard; if any have them they should have them off)….” 
A brief perusal of pictures from the Southern States Mission’s newspaper in early 1899 suggests that something like 70% of travelling Elders were clean-shaven, 20% had a moustache, and 10% had a full beard or Van Dyke. 
The “Southwestern States Mission” series (homepage) examines mission life in (mostly) Texas around 1900.
 Entries mentioning shaving: Brooks: 15; Clark: 24; Duffin: 1; Folkman: 18; Forsha: 5; Jones: 81.
 144 entries in the diaries explicitly record shaving; distributed across six diaries, we can calculate 138 intervals between recorded shaves by a particular missionary. The smallest interval is 2 days; the largest is 233. 58 (42%) of the intervals extend 7 or fewer days; 36 (26%) are for 8-14 days; 26 (19%) are for 15-35 days; and 18 (13%) are for 39 or more days. (A more complete breakdown of [interval:# of instances]: 2: 3; 3: 4; 4: 11; 5: 16; 6: 12; 7: 12; 8: 7; 9: 8; 10: 5; 11: 4; 12: 2; 13: 4; 14: 6; 15-35: 26; 39-233: 18.) Some of the data seems to center around an interval of five days, but not so strongly that we can assume the missionaries simply failed to record their shaving in the longer intervals.
 I conjecture two factors that might partially account for seasonal variation: the (in)convenience of shaving and illness. Summer illness might make Elders less likely to shave and/or write about it in their diaries. In the winter they would need to heat water or shave with cold water, both of which increase the likelihood of a diary mention. Unfortunately for this hypothesis, it’s pretty warm in East Texas from March to November, and intermittently so the rest of the time. Recorded shaves by quarter: Jan – Mar: 50 (35%); Apr –Jun 40 (28%); Jul – Sep 16 (11%); Oct – Dec 38 (26%). Recorded shaves by month: Jan: 15 (10%); Feb: 13 (9%); Mar: 22 (15%); Apr: 16 (11%); May: 14 (10%); Jun: 10 (7%); Jul: 4 (3%); Aug: 7 (5%); Sep: 5 (3%); Oct: 13 (9%); Nov: 10 (7%); Dec: 15 (10%)
 Recorded shaves by day (total = 144): Sun: 8 (6%); Mon: 11 (8%); Tue: 18 (13%); Wed: 26 (18%); Thu: 21 (15%); Fri: 15 (10%); Sat: 45 (31%).
 Morning shaves: 81; afternoon: 47; evening: 11; unspecified: 4.
 Out of 144 shaves, 24 (17%) happened on the same days as a bath and 10 (7%) happened on the same day as a haircut. In 3 instances (included in the totals above) the diary indicates shave, bath, and haircut. Not all of the haircuts and shaves were for the same person, eg: “After eating we shaved and I cut Elder Huntsman’s hair.” (Brooks, 1900 Mar 06 Tue). Examples of coincidence with other chores: “After breakfast we wrote our Journals, had a shave, Etc” (Forsha, 1900 May 25 Fri); “spent the forenoon in Cleaning Cloths Shoes and Shaving.” (Forsha, 1899 Dec 31 Sun).
 I count 99 (69%) instances of shaving at an occupied house, 10 (7%) in some other type of building, 32 (22%) outside, and 2 (1.4%) unspecified. Shaving “at” a house did not always mean shaving inside; they might still go to the creek to shave, whether to not impose on the host or because that is what the host did. “Slip in the timber”: Clark, 1900 Nov 08 Thu. Examples of other arrangements: “We went on a ways farther, got out in the woods out of sight and shaved.” (Brooks, 1900 Mar 24 Sat); “we continue on and go in the School house and have a Shave” (Clark, 1900 Nov 19 Mon); “we continue our work and come to a patch of timber and make a fire and warm and have a Shave” (Clark, 1900 Dec 15 Sat); “Fair weather we go to work then we go down in the timber bottom and have a Shave where there is Some water” (Clark, 1900 Sep 26 Wed); “it Began to Rain and we went in a old house and got out of the Rain while there we had a Shave when it got through raining we went on visited Some more” (Clark, 1901 Mar 08 Fri); “cold norther. we leave mr Stoveall and go to Canvassing go nearly all day without any dinner or Supper we Stop by the road and Shave then we go over to the School house and fill our appointment” (Clark, 1901 Mar 20 Wed).
 I count 81 instances (57%) when the Elders shaved at the house where they had stayed the previous night and 59 (41%) when they shaved at a house “on the road,” with 3 (2%) unspecified.
 Examples: “Had a bath and shave and a general clean up for Sunday. Stayed with Bro. Burnett at night.” (Folkman, 1901 Nov 30 Sat); “Went to Bro. P. Odom’s. I half-soled my shoes and shaved and got ready for Christmas.” (Folkman, 1901 Dec 24 Tue); “After partaking of a nice dinner, we talked for a while and then I packed my grip and made preparations to bid farewell to Texas. Elder A. and I shaved each other.” (Jones, 1902 Feb 13 Thu); “After dinner I shaved Bro. K. and Elder H. as they were going to the Dallas fair.” (Jones, 1900 Oct 10 Wed).
 I find only three instances of using a barber in connection with shaving, all from Elder Jones, and only one where he went to the barber for a shave. “We went to the barber shop and had our razors sharpened.” (Jones, 1901 Jun 03 Mon); “…we went to the barbershop and had a shave, 15c, and then walked out to Bro. Griffin’s….” (Jones, 1902 Feb 11 Tue); “Went to the barber shop and got our hair cut. The barber gave us a shave free gratis as we were ministers and do free work.” (Jones, 1901 Jun 17 Mon).
 The whole paragraph: “Special regard should be paid to dress and appearance. Your success largely depends upon the impression you make when first meeting the people; if shabby and unkempt in appearance, the impression you make will be unfavorable. The wise Elder will always keep his clothes well brushed and sponged, shoes blacked, teeth brushed, face cleanly shaven at least twice a week (never wearing a big Cossack beard; if any have them they should have them off), and body sweet and clean by bathing often in pure running water or in a tub. Never remain in the water longer than five minutes at a time in this climate. Avoid stagnant pools and deep, dead water as you would a pest house. Heed these suggestions if you would preserve your health.” The letter was sent in 1896, four years prior to the start of the study period, from Kansas City, MO, which, after boundary realignment, would become SWSM headquarters in 1901. Samuel G Spencer, “To the Presidents of Conferences and Traveling Elders,” Kansas City, Mo.: Northern States Mission, 1896, 4 p. Brigham Young University, L Tom Perry Special Collections, Americana Collection, BX 8608 .A1a no.1305.
 Latter Day Saints Southern Star, Chattanooga, TN, Vol 1, No 1 – 29 (1898 Dec 03 — 1899 Jun 17). I counted only photos of then-current travelling elders. Note that this was a very quick survey and that the Southern Star printed pictures of conference presidents almost exclusively, so the photos are not a random sampling. 37 men are pictured, 29 of whom were travelling Elders: 21 clean-shaven, 6 moustaches, 1 Van Dyke, 1 beard.