In case you don't have it I think this is Douglas' grave https://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=Horstead&GSbyrel=all&GSdyrel=all&GSob=n&GRid=134641419&df=all&
https://www.familysearch.org/search/record/results?count=20&query=%2Bgivenname%3AReginald~%20%2Bsurname%3AHorstead~ England and Wales Birth Registration Index for Reginald
https://www.familysearch.org/ark:/61903/1:1:4DZM-36Z Census record that shows a Reginald and brother Douglas and parents in England slightly different spelling of last name but everything else seems to fit
I also checked both WWI and WWII records for Canadian military and while I found a number of Horstead listings none were Reginald born in England or in 1887. I checked death records and service records
http://www.bac-lac.gc.ca/eng/discover/military-heritage/Pages/military-heritage.aspx
https://aad.archives.gov/aad/display-partial-records.jsp?f=5058&mtch=7&q=Horstead&cat=all&dt=3001&tf=F I also checked WWII US records no Reginald and WWI via a pay site.
There is a Reginald H and a Reginald S which upon opening file is Stanislaus so your guy , It says he was born in Portsmouth England.Sept 30 1887. At the time of this document he is not married. His occupation was teamster. The document is dated Aug 31, 1915. He is 5' 3' chest is 38' 144 pounds. Eyes blue hair is light brown. He is listed as Roman Catholic. He is deemed fit. No distinctive marks or illnesses. He is attached to the Overseas Expeditionary Service. Final signature in Nov 5, 1915. It says 37th Regiment and his enlistment number is 195102. He served in France. His last shots were given Aug 1918. So he seems to have survived the war. In later papers he is in the 93rd Battalion.
Date for leaving France is listed as Aug 30 1918. but another page says unit sailed July 15, 1916 from Halifax on S S Empress of Britain.
He appears to have been examined several times by medical personnel but it is really hard to read why... the last time was April 9, 1819. The location ends with the word dale and it looks like it starts with maybe an S? There is another document that says he was a bartender in Canada. It says he has a problem with his spine (I think due to an injury in the war) that makes it difficult to carry a pack without pain. This is dated Oct 14, 1916. The diagnosis is http://www.mayoclinic.org/diseases-conditions/kyphosis/basics/definition/con-20026732
In these pages his parents are both listed as dead.
He was given the British War and Victory Medals
He was discharged on May 27, 1919 in Toronto Reason "demobilization" He has an address of 407 Gerard Street E in Toronto at time of discharge. 31 years 7 months at time of discharge. Says proposed residence Petersboro after discharge.
His military will gives all his effects to Norman Horstead Royal Cambrian Institute of Deaf and Dumb Swansea England. It does not indicate who this is. Another person mentioned other than his brother Douglas was an Alfred on another document and no indication of relationship.
I saw nothing in this file about his death.