I really like what Kalen had to say. And, the only source I have to really try to analyse the frequency or willingness of the guys in late 1800s to go out and play the toon-a-mints in wild and whacky weather would be the "Scrapbook of Old Tom Morris". I'll have to look through the clipping and try and find any accounts and descriptions specifically of wild weather. My previous readings were not specifically looking for the wild weather issue to try and get a handle on how the old guys approached the subject. Melvyn's account of Young Tom playing in snow is the only specific example I have heard to consider just how brutal of weather they would accept as just the rub of the weather and conditions of the day, and go play whatever you are dealt.
I also suspect as Kalen discussed, matchplay lent to the playing ethic, that 'it is the same' for each opponent, no matter what the weather - just play.
Another factor I think has had an impact on modern day attitudes is the shear size of the fields in tournaments, putting pressure on the tournament organizers to get the rounds in as the size of the entrants in the field increased.
but, that doesn't answer the original question of what influence the wild yet expected traditional weather generally is there in the craddle of where golf developed, on the trends in architecture. To that end, I think the design meld of randomness of bunker placements, as is the randomness of weather conditions cropping up at any time, is sort of a marker for the whole design/lay-out mentality up to a certain era, where you get what you get, and just play on. Then, when tournaments got more organized with larger fields of contestants, there might have been more emphasis on more considerations to more fully design features to aid, or make the playing field more compatible with predictability of playing conditions and reactions of how the ball and impliments would be effected by the design.
So, I think we may have had randomness, play on, take what you are given by nature in the earliest days, and then when things got more organized, larger fields, more ability to build and control the field of play, a concerted effort to blend design "fairness-predictablility" into the newer designs effecting more considered hazard placements for a specific purpose, and to demand a specific player skill set based on the archie's 'original intent'; not Mother Natures ambivolance.