I'm not an expert, but don't you need a lot more linear feet of trench than you need of well? To demonstrate, if you lay on 40 degree earth then 40 degree water which one make you colder first?
Sure, trenching is cheap, but from my understanding it take oodles of it...
In your example the variable of contact is included, as water would contact nearly all of your body and the ground less than half. If you were covered in 40 degree dirt to the same level I suspect you would see very little difference in the time it took to make you uncomfortably cold.
Water does transfer heat well, but there is usually only 20-30 feet of water in a well leaving the rest of the depth for air contact which is an even worse method of heat transfer than either of the other two. Thus, you have an average heat transfer with which to compare to the more constant transfer of heat by contact with soil alone. Even if it required more footage, the cost of trenching to below the frost-line is less than the cost of a well. Given the area in which Denni lives does not have a very deep frost line and an estimated well depth, which I assumed a similar aquifer level from that in a similar area, the trenching would be a cheaper and more reliable estimate. The wells may have to go much deeper to find sufficient water and new wells being dug will affect the water level in an existing well, as would any use of explosives in larger scale construction.
With that said, the farther north you travel the possibility of the well being a better choice rises so any such decision would have to be based on the very specific location options.