What time was it in Dawson Creek, BC at 1900-01-01 00:00:00 +0000?
The pedantically correct answer, based on the IANA Timezone Database, is that it was 1899-12-31 16:00:00 (-0800) at 1900-01-01 00:00:00 +0000. The IANA time zone entry for America/Dawson_Creek is shown below.
# Zone NAME GMTOFF RULES FORMAT UNTIL
Zone America/Dawson_Creek -8:00:56 - LMT 1884
-8:00 Canada P%sT 1947
-8:00 Vanc P%sT 1972 Aug 30 2:00
-8:00 - MST
Dawson Creek was officially no different than any other place in British Columbia prior to Aug 30, 1972. Since British Columbia nominally switched to the Pacific time zone (-0800) in 1884, and since nobody has ever had daylight savings time on New Years Eve or New Years day, it was 1899-12-31 16:00:00 (-0800) at 1900-01-01 00:00:00 +0000. This pedantically correct answer has to be taken with a grain of sand, however.
History of Time Zones
The 1884 switch from Local Mean Time to Pacific time is based on the 1884 International Meridian Conference, held in Washington, D.C. The United States and Canada faced a mutual problem in that they spanned multiple time zones. Railroads were the driving force behind standardizing time, and Canada was one of the leaders in this regard.
Sir Sandford Fleming, then the director of the Canadian Pacific Railway, was the driving force behind Canada's time zone standardization. The last spike connecting the Canadian Pacific Railway with the rest of Canada was driven in 1884, with Fleming in attendance.
source: https://en.wikipedia.org/wiki/File:LastSpike_Craigellachie_BC_Canada_-_cropped.jpg. Fleming is the tall gentleman with the tall hat standing behind and to the left of Donald Alexander Smith, who is driving in that last spike.
Fleming had previously proposed a single time used around the world centered on what is now the 180th meridian. This would have placed the awkward astronomical switch at noon from one day to the next in the middle of the Pacific Ocean. This never caught on. The solution accepted at the 1884 conference, which Fleming attended as the representative of Canada, was to make the Greenwich meridian the center of everything time-wise, and to switch the transition from one day to the next from noon to midnight. This is the origin of what we now call UTC (Coordinated Universal Time).
The 1884 conference did not mandate splitting the world into time zones. This was left up to individual countries, and within countries, subdivisions of those countries. The southern portions of Canada, which were already interconnected by railroads, had already done that, at least unofficially, and at least for those portions of Canada interconnected by railroads and telegraph lines.
If I was a farmer in BC, Canada in the year 1900, what would I set my pocket watch to?
The first train came into Dawson Creek in 1931. Even if a settler had a pocket watch, there was no way for him to synchronize it to some standardized time. There was no internet, no radio, no train, no telegraph. Whether there were any settlers in Dawson Creek on New Years Day in 1900 is dubious. The Canadian government opened the Peace River District to settlement seven years later. To the very few people in the vicinity Dawson Creek at that time who cared about details such as minutes, it was about 20 minutes after sunset on New Year's Eve, 1899. To the rest of the people there at that time, it was a bit after sunset, but well before it was too dark to see.
If a settler in that area did have a pocket watch, he might have been able to synchronize it with respect to local noon. If the settler was educated enough to have known about the equation of time (and to have cared about the distinction), he might have incorporated that into setting the watch so as to make it follow local mean time as opposed to local solar time. Until time-synchronized commerce became common, local solar time was a better indicator of the time of day than was mean time adjusted to a time zone.
The above is not meant to disparage farmers and settlers. Read the writings of Robert Service and Jack London, neither of whom was "uneducated". Admittedly, they were writing about a locale even further north than Dawson Creek, but not that much further north. Neither Service nor London worried that much about time. They worried about surviving the winter.
Asking what time it was in some place where people did not care about measuring time with respect to a clock in Greenwich, England, and couldn't have done so even if they cared to do so is a bit silly.