It's not possible for a lot of people either, but you're just making one check to cover a long period of time (do you make checks every 50 feet?) for one, while completely disallowing the other. Both are impossible.
I don't think you're realizing what 2 feet actually is. You're telling me that as a 10 year old, you walked through mud that came up to your waist? Not buying it. As someone who grew up on a farm myself, and seeing countless times how 1 foot of mud stops grown adults in their tracks. And as someone who in my young adult life did land nav courses that are very similar to what PCs would do just going from one point to another on a map, there is 0% chance most adults could do most of those tasks (climbing, hiking in swamps or through thick forest or up steep hills, rope use, etc.)
The point is, 99% of the time in the game, we either just enforce a passable check for PCs that have zero chance if we were to apply any sort of realism to the scenario*. But suddenly when it comes down to something like this, then it's automatically "no way! Not possible! Not realistic!"
*And that check covers a long time instead of being repeated as often as it "should" because it's not fun in the game to just sit there and keep making dozens of die rolls over and over. I.e., we like to handwave away realism for the fun of the game, but then want to enforce it arbitrarily other times. Why? If it's taking away the fun of someone, why do we handwave it away for the fun of everyone else?