To my eye, the bunkering at White Bear is well preserved and a perfect example of a course of it's vintage. What I mean is that if you look at aerials of other golden age courses in Minnesota, the bunkering scheme is not obvious. It seems random with bunkering scattered in different locations as well as varying in size and shape.
As Morgan noted above, a number of bunkers were removed from the area surrounding the 7th and 8th greens and replaced with shortgrass. I think there are other opportunities to do that elsewhere, with unoriginal bunkers such as with the right greenside bunker at the 17th.
We are clearly in an age where bunker aesthetics mean a lot, either on new construction courses built by Messrs. Doak, Coore, Hanse, etc. or on renovations on classic courses which are often sold on moving bunkers to be "more in play", ease of maintenance, or to "frame" a hole. However to me sometimes these bunker renovations can cause the hazards to lose much of their character.
The bunkers at White Bear are all very unique in their own ways.
Would the 1st hole be better without the cavernous greenside bunker?
Some, such as the pulpit bunker short right on the 3rd are an incredibly difficult recovery, in this case because it is only about 4 feet wide.
Some are visually very imposing, such as the fairway bunkers on the 16th which are surrounded in tall grass and must be carried to set up an ideal angle to the green on approach.
Some bunkers such as the one behind the 11th, are shallow but in a way that the best play toward a pin on the 11th green is a putt.
As Mr. Doak notes above, the bunkering on the 12th hole is nearly perfect. Depending on the location of the pin, a player might need to flirt with the right row of fairway bunkers, or if playing away from those, the player has to hit over, but close, to two cross bunkers short of the green. Bunkers behind the green gobble up overly aggressive approach shots to the green that falls away from the player. Some trench bunkers (long, skinny) can help a player stop their ball from rolling off a steep hill.
Correct me if I am wrong, but wouldn't bunkering located in somewhat random location be ideal as it allows the course to play differently in different weather & wind patterns?
That being said there has been a big effort, particularly last season, to bring the shortgrass closer to bunkers. For example, fairways bunkers at the 2nd and 13th had previously been floating in rough, but are now on the edges of the fairways.
In terms of the aesthetics of many of the bunkers, generally speaking they fit well with the overall maintenance of the golf course. Part of White Bear's charm is that it is a bit wholly and rough around it's edges. The greens don't stimp at 12. "Perfect" or "tournament" level maintenance has a place at some clubs (Hazeltine), but it would take away from the White Bear experience in my opinion.