A bit pressed for time, so I'm going to give you the abridged version of things. One thing here is that what you're talking about above that you like is a wargaming aesthetic of (1) suss out the GM’s conception of the situation in the imagined space > (2) figure out how best to game that mental model by putting together a gambit with an attenuated risk profile and/or one making a proposition that the GM will agree with sans rolling dice. That is certainly one aesthetic of play, but it is definitely not the sort of play that Mouse Guard (and kindred games) design for. Mouse Guard is designed for big, bold moves by the members of the guard. The have to prove their mettle to themselves, to their superiors, and to everyone in the Territories. The game engine requires failure to power character advancement and one of the most important currencies (Checks) use for doing all the stuff on The Player's Turn (down time in a safe haven) is gained by using your Traits against you...and you also have to be ware of your Nature advancing too high so there is a balance of keeping it in check also. This game is about big, bold moves, overcoming obstacles, failing and finding out who your Mouse is, changing and evolving, and carrying on or succumbing to the hardships of life as a member of the Guard (or retiring).
This is not a "minimize risk profile" sort of game or a "try not to roll dice" kind of game. This is also not a "no PvP" game. This game encourages it (and its easy to resolve), but not "to the death" kind of stuff (arguments, scraps, stuff like that)! Its a game about making big moves, overcoming obstacles and setbacks, and doing a whole lot of heroing in service to your Mouse Guard duties and the good folk of the Territories. In the course of that your PC will evolve and we'll find out who they are.
Missions - These are Adventures in D&D or Torchbearer parlance or Scores in Blades in the Dark parlance. There are 10 Mission Archetypes like there are 6 Blades' Score archetypes. Missions consist of 3-4 situations related to Weather, Wilderness, Animals, Mice (typically pick two per mission and use reserves for Twists) + putting one or more of the PC's thematic flags (Goals, Beliefs, Instincts, Relations etc) in the crosshairs. The GM frames the situation > there is a back and forth to firm it up as needed > GM and players suggest actions to resolve things and once set a Test is settled upon > Obstacle is set via the rules (this is the "Don't Be a Weasel" part...once the Obstacle is factored up, the dice are going to be rolled....take a look at that first paragraph for incentive to make tests) > dice pool is martialed from the multifaceted means of the Mouse Guard > Test is made > result is success and situation resolved (move to next situation) or Condition and situation is resolved (moved to next situation) or Twist where something compelling happens to escalate the present situation or change things adversely to test the Guard (Twists should virtually always be about thematic PC flags like putting two PC Beliefs in conflict so maybe they'll fight!...or making a PC prioritize either their Relation or the welfare of the settlement/the Guard's duties etc).
After the initial Mission is resolved (which is handed down straight from the Matriarch to springboard play), play goes from GM's Turn to Player's Turn. They'll be at a safe haven somewhere when their turn begins. The next mission will evolve organically from some stuff that happened in the last Mission or stuff that happened during player Tests (Checks are cashed in to make Tests to do all kinds of things from recover conditions/gear to attain gear/supplies/aid to call upon allies to investigate stuff to mediate squabbles or get married or find/make friends to carry out little mini-adventures and all kinds of stuff), typically from a resultant Twist (and typically if the session ends on that Twist).
At end of session we go over things together and assign Fate and Persona (currency to do stuff) based on that session's interactions with Beliefs, Goals, Instincts, MVP, Workhorse, Embodiment.
The game carries on like this through the seasons. We get to Winter and its a special season where we do Rest & Recover, Age, Practice, Reflection, Promotion, Retirement, Memorials. After that is Unfinished Business which is a long bit of free play where players dictate the content of play like an extended Player's Turn but without the cost of Checks for Tests but there are two catches; they can't recover conditions and whatever they want to accomplish must be in Lockhaven (so no patrols/journeys to other settlements). We play through a bunch of tests/conflicts of the players desiring, focusing on stuff that they're interested in that didn't get the full focus or perhaps tightness of focus that they were looking for.
After that its another end of session like above (Beliefs, Instincts, MVP, Workhorse, Embodiment).
Anyone who has played/run Torchbearer will recognize this stuff (only reskinned). Mouse Guard is a stripped down Torchbearer with a different focus and theme. There isn't delving. There isn't the brutal focus on inventory/gear/attrition/light. Its Patrols and Mail Delivery and Trailblazing and Hunting Predators and Pathfinding and Dispute Mediating and all the other kinds of stuff Rangery/Knight-types would do.
But to get back to your initial post:
* This isn't a wargaming aesthetic where you're trying to suss out the GM's mental model of situation/imagined space in order to reduce risk profile to 0 or get out of rolling dice (you want to roll dice in this game).
* GM doesn't dictate the approach to obstacles (though they absolutely will make suggestions and heavily foreground conflict and telegraph dangers/opportunities). Players have all the typical say in making Tests to resolve obstacles on the GM's Turn (or maybe getting some PvP action in if they have a dispute over how to proceed and someone needs to be convinced or socked in the mouth!).
* Obstacles are factored via a codified game engine. This isn't like 5e D&D where the GM just sets a DC at their discretion/conception of the imagined space. You describe a situation and there will be a base number for a test and if other stuff applies, it goes up by that Factor until an Obstacle Factor is reached. Versus Tests are just like they sound. One dice pool for a player is martialed against an NPC (or another player) dice pool and they're compared.
* Yes, once an Obstacle rating is factored up, players don't get to back down their PCs from the test. Roll the dice and suck up the success or consequences (again, failure is awesome and necessary for advancement in this game)!
LOL at my "abridged version of things."