You've misunderstood the nature of the GM's and Players' Turns. Node-based prep in the Alexandrian style doesn't really apply.
I don't super blame you, I don't think there's any nomenclature they could have used that wouldn't have been too esoteric to remember or too generic to remember accurately. But:
[The GM] gets to describe where the mission begins, what the players have to do and in what order it must be done. [The GM] gets to confront the characters with weather, wilderness, animals and mice.
In order to overcome these obstacles and complete their mission, the players must test their abilities and skills. The GM gets to say which abilities and skills are tested. This part of play is called the GM's Turn. [...]
After [the GM is] done beating up the guardmice, usually once they've completed their mission, reached the safety of a town or passed a dramatic moment in the story, the GM hands the reins over to the players.
The game then enters the Players' Turn. During this part, the players drive! They get to try to recover from the beating they took in the GM's Turn. They can also try to pursue some of their own personal goals and needs without the GM getting in the way.
-- "The Mission", p.65 of Mouse Guard 2nd edition
In this case, "turn" refers to who has initiative in presenting obstacles. To illustrate, let's say there was a mission with mystery elements - a notable guard sympathizer has vanished from a fiercely independent town, and the Guard are tasked with tracking them down.
As the GM, you would decide the truth of the matter - say, the sympathizer was left to fend for themselves during a raid and carried away into the wilderness, and the town is covering it up - and pick two major obstacle classes, let's say "mice" and "the wilderness". The guardmice have to find someone in the town willing to give up what happened, and then make it through the wilderness with sufficient speed and awareness to spirit their target away from their captors without a confrontation.
In the GM's Turn you would aggressively present these obstacles to the mission, rather than leaving them up to the guardmice to discover in a neutral investigative position. If the guardmice can't pass tests or win conflicts against the obstacles you initially present, you don't just shrug and ask them what's next, you reply to failures with twists and conditions. Hand out a condition as a price for success, or use a twist to introduce a tangential obstacle.
It's only the Players' Turn when the mission is over with, successfully or not. Generally, complex mysteries don't really come up during the Players' Turn -- the players are trying to recover, advance their goals, and otherwise practice their skills.
Node-Like Prep
However, you can still perform prep in a node-based style even though you're not presenting things to the players as a mystery. You might see multiple paths forward - for instance, guardmice might canvass the town for a guard supporter, abandon the townsmice and try to investigate the obscured evidence for any clues that survived, or openly call out the town for abandoning a fellow mouse, starting an oration conflict. Each of these paths could become a node in prep leading to the wilderness obstacle.
Or, you could prep some reasonable twists. In this case, one of the parallel nodes in the diagram would represent a "golden path" where the players do everything right, and you'd document the twists you had cooked up as its sibling nodes. Failing to follow tracks through the wilderness means a (slightly modified) journey conflict as the mice comb the wilds for clues with no friendly place to resupply. Failing to be aware of the captors' movements means a fight conflict against them to get the supporter out safely.
Finally, when you're preparing, keep in mind obstacles can occur at varying degrees and the categories you're picking are the two major ones. Animals and the weather don't somehow stop being problems because the GM wants to focus on other things, they're just there on the backburner to show up in lesser forms, perhaps as twists, or, especially in the weather's case, just as a complicating factor adding an Ob or two to something the guardmice are already trying to do.